Video lectures of mathematics courses available online for free It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some universities do that (albeit to a very limited extent), and I hope we can compile here a list of all the mathematics courses one can view in their entirety online. 
Please only post videos of entire courses; that is, a speaker giving one lecture introducing a subject to the audience should be off-limits, but a sequence of, say, 30 hour-long videos, each of which is a lecture delivered in a class would be very much on-topic. 
 A: Here is an ongoing series of videos covering Point-Set Topology that is planned to continue indefinitely.
A: The Eilenberg Lectures at Columbia.  So far, the topics have been:


*

*Benedict Gross, on number theory and representation theory

*Edward Frenkel, on Langlands program and quantum field theory

*Sergiu Klainerman, on the mathematical theory of general relativity

A: A great collection of combinatorics videos
Igor Pak’s Collection of Combinatorics Videos
A: Eleven lectures by Amritanshu Prasad on representation theory, the first two on generalities, the next five deal with representations of symmetric groups in the semisimple case, going up to the calculation of character values using Frobenius' formula. The next two deal with polynomial representations of GL(m). The last two are on the hook-length formula and Frobenius's characteristic function respectively. Assignments and notes are available on the course website for the first seven lectures.
This content forms the bulk of a book titled "Representation Theory: A Combinatorial Viewpoint" (Cambridge University Press, 2015) by the lecturer.
A: Lectures on Real Analysis, from Bilkent University (Assoc. Prof. Dr. Alexandre Gontcharov): http://video.bilkent.edu.tr/regenerated_pages/Mathematics_ms.html
A: MSRI's online videos. These do not consist of courses, but each semester is themed so the videos offer good exposure to many areas of current research.
A: Master Class on Wall-Crossing. Lectures given by Maxim Kontsevich.
A: A real analysis course from Harvey Mudd College. An early course for math majors, so it also covers a bit of good proof writing techniques, induction proofs, logic, etc.  
(Disclaimer: Filmed by me. So you know who to blame for the bad camera work.)
A: There are many good quality math lectures (mostly in Russian but sometimes in English)  http://www.lektorium.tv/  they are grouped by courses (for example http://www.lektorium.tv/course/?id=22876)
A: I am teaching a course on "Free Probability Theory" this term (winter term 2018/19). The videos will appear progressively here.
A: Ted Chinburg has videos of his lectures for what is going on a 2 year course in algebraic number theory online( direct links to videos: semester 1, semester 2, semester 3, semester 4), and from there you can also get lectures from various seminars at Penn.
Also, there's the MSRI database for all the things that go on there, they're all over the website at each program's site.
A: Sets, Counting, and Probability, taught by Paul Bamberg at Harvard. 
A: A bit borderline since its only nine lectures, but a mini course on Additive Combinatorics taught at IAS by Boaz Barak, Luca Trevisan, and Avi Wigderson. 
A: The San Francisco State University hosts large number of course videos on various subjects
including: 
$\cdot$42 videos on Coxeter Groups
$\cdot$41 videos on Discrete Geometry
$\cdot$18 on Dynamical Systems
$\cdot$16 on Lie Algebras
$\cdot$43 on Matroid Theory
$\cdot$28 on Real Analysis I and II $\ldots$
All you need to do is click on the drop down menu "List all courses".
A: The courses of the summer school Poisson 2012 (that took place in Utrecht), as well as lectures of the conference that followed, are available online: http://www.youtube.com/user/poissonutrecht
The courses are: 


*

*Poisson and Symplectic Geometry of Moduli Spaces of Flat Connections, by Anton Alekseev 

*Poisson Geometry, by Rui Loja Fernandes 

*Lie Groupoids and Multiplicative Structures, by Henrique Bursztyn 

*Cluster Algebras and Compatible Poisson Structures, by Michael Gekhtman 

A: 77 videos on Category theory.
A: The lecture videos of Introduction to Abstract Algebra, taught by Benedict Gross at Harvard, can be downloaded here.
A: Search iTunesU for "Mathematics": It turns up many courses (I couldn't see how to count them easily), including the Gilbert Strang course already mentioned.
A: Differential Equations, taught by Arthur Mattuck at MIT. 
A: Twenty-four lectures from a course on algebraic combinatorics, taught by James Propp.
A: Might as well plug my own course on Diophantine Geometry. It's in Portuguese, so that will restrict the audience a bit, but I am having fun and it's nearly finished (last class on Nov 8th 2011). IMPA has a bunch of other videos as well, just follow the links.
http://video.impa.br/index.php?page=programa-de-doutorado-2011-geometria-diofantina
A: I would recommend those from Simon's Center for Geometry and Physics. Here is a list of all workshops at SCGP.
Videos from all of their workshops are available online.  Here are all talks from Random Tilings Workshop last February.
A: If it's not too gauche to plug my own course at CMU,
23 lectures on Analysis of Boolean Functions (one lecture by John Wright):
http://www.cs.cmu.edu/~odonnell/aobf12/
A: Federico Ardila's (full-semester) courses on
polytopes,
combinatorial commutative algebra,
Coxeter groups,
combinatorial Hopf algebras, 
matroid theory,
and enumerative combinatorics. They include lecture videos and lecture notes.
See http://math.sfsu.edu/federico/teaching.html
Now they are also on YouTube here:
polytopes,
combinatorial commutative algebra,
Coxeter groups,
combinatorial Hopf algebras, 
matroid theory,
and enumerative combinatorics. 
A: My alma mater, the University of Colorado at Colorado Springs, has a video course archive on some subjects (mostly undergraduate). These include
Calculus I, II, III
Differential Equations (undergrad and grad)
Linear algebra (undergrad and grad)
Discrete Math (undergrad)
Algebra (elementary and abstract)
Analysis (Real, Functional, but no Complex)
Statistics (graduate)
Geometry (mostly Euclidean)
There are several more.
For each class here, the entire semester was recorded.
To download the videos, you have to create an account, which merely requires a name and email address.
Here's the webpage:
https://www.uccs.edu/math/vidarchive.html
A: Thirty lectures from the course Wavelet Theory given at the University of Maryland by John Benedetto. 
A: LMS Durham Symposia have archive of videos online which can be found at http://www.maths.dur.ac.uk/events/Meetings/LMS/
For example, 2009 conference on model theory of fields has videos of the talks by Hrushovski, Kazhdan, Macintyre and Zilber, among the others.
A: Here a summer school on representation theory for $SL_2(\mathbb{R})$:
http://www.math.utah.edu/vigre/minicourses/sl2/
Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry":
http://www.uni-math.gwdg.de/aufzeichnungen/SummerSchool/
Algebraic Quantum Field Theory - the first 50 Years
http://www.uni-math.gwdg.de/aufzeichnungen/AQFT50/
A: nice videos about Quantum Mechanics (By J.J.Binney -Oxford),  total 27 videos with about 1 hour duration, and QFT (By David Tong - Cambridge). Those videos about QM are really great here. 
A: Thematic Program on Topology and Field Theories, Summer 2012, 34 Lectures.
A: Joyal's mini-course on topos theory at IHÉS: 
Clicky
A: Just found the very stimulating lectures by prof Alan Huckleberry at Bremen;
Differential geometry
Complex Analytic and Algebraic Geometry
Foundations of Mathematical Physics
A: *

*30 lectures on Lie Groups, Representation theory and Symmetric Spaces by Wolfgang Ziller, UPenn

*27 lectures on Algebraic Topology by Pierre Albin, University of Illinois

*36 lectures on Topology & Geometry by Dr Tadashi Tokieda

*28 lectures on Differential manifolds and Lie groups (Lectures on Geometrical Anatomy of Theoretical Physics) by Frederic P Schuller

*50 lectures on Linear Algebra Done Right by Sheldon Axler

*15 lectures on Ricci Flow by Bennett Chow at MSRI
A: Here are some of my favorites :

*

*Sidney Coleman's Quantum Field Theory


*Shiraz Minwalla's String Theory


*MIT OCW


*Videos to short courses at some workshops can be found at IAS and MSRI
A: For what it's worth, my own University of Toronto 2009 course on Algebraic Knot Theory.
A: Gilbert Strang's course on Linear Algebra at MIT. 
A: Two courses by Gilbert Strang: Computational Science and Engineering I and Mathematical Methods for Engineers II. 
A: David Forney's course on Coding Theory at MIT. 
A: The University of South Florida has a whole series of lectures devoted to numerical methods here: http://numericalmethods.eng.usf.edu/videos/
A: A master course by Benoit Fresse on operads and Grothendieck-Teichmüller groups (in french), at Université Lille 1, given this semester (Winter 2012).
The course has a really nice and complete introduction to the subject. The principal reference is a preprint (in english) writed by Fresse.
A: Andrew Ng at Stanford offers videos of various courses.
A: A Computability Theory course by Bart Kastermans.  These lectures followed Robert Soare's new book, which is not yet published, so they are temporarily behind a password; however, Bart's website indicates that the passwords are available upon request. (In any case they will be open to the public eventually, I think.)
A: My rather standard course on ordinary differential equations, at http://drorbn.net/index.php?title=12-267.
A: The videos of Mike Freedman lectures on the topology of 4-manifolds, broadcasted from UC Santa Barbara: Freedman's Lectures
Also other videos on 4-manifolds and related topics given at MPIM during the 4-manifold semester in 2013: MPIM lectures
A: The YouTube channel of The Institute of Mathematical Sciences, Chennai has several such courses, such as "Effective methods in Diophantine Analysis" by Yuri Bilu, "Soergel modules and Kazhdan-Lusztig theory" by Ben Elias, a course on von Neumann algebras by Sunder, Lie groups by Raghunathan and many more:
http://www.youtube.com/user/matsciencechannel/playlists
A: The Hausdorff Center for Mathematics in Bonn has a lot of videos online on their youtube channel.
A: For elementary courses, say up to first year undergraduate or so, Khan Academy has a wide range of courses on maths (some of which are listed under computer science or physics).
For graduate courses, several answers have mentioned MSRI and/or the Hausdorff institute but the Fields Institute video archive deserves a mention as well. The archive does no go back very far, but there are some excellent courses at various levels. (Search for the word "course" on the linked page).
A: Algebraic topology by Prof. N J Wildberger of the School of Mathematics and Statistics, UNSW
A: The Fourier Transform and Its Applications, taught by Brad Osgood at Stanford. Lecture notes here.
A: Miles Reid's lectures on Algebraic Geometry and Algebraic Surfaces.
A: At my YouTube site Insights into Mathematics. I have playlists on
Rational Trigonometry
Linear Algebra
Math Foundations
History of Mathematics
Universal Hyperbolic Geometry
Algebraic Topology (this was mentioned above)
Elementary Mathematics (K-6)
A: There are lots of links to various pages filled with online video lectures here.
Go to "Links" on the left hand side.
Some of the links are broken or out of date, but there's still a ton of good stuff here.
A: Very, very introductory lectures in complex analysis: http://adamglesserf09math481.wordpress.com/page/3/
A: Eight recent lectures by Emmanuel Candes on compressed sensing are linked to from here: http://www.newton.ac.uk/programmes/INI/iniw04p.html
More generally, the Newton Institute has been making a large archive of talks available.
A: If you happen to know Italian, on Massimo Gobbino's home page there are videos (tablet pc screencasts + audio) of several courses (Calculus I and II for engineers, honors calculus/analysis) and lots of high-school Math Olympiad training material.
Highly recommended: I find tablet screencasts an excellent medium, and on top of that Massimo is a great teacher.
A: Here is a summer school on Berkovich spaces
http://www.diffusion.ens.fr/index.php?res=cycles&idcycle=490
(there are more courses at http://www.diffusion.ens.fr/ but unfortunately they are not broken into categories; one has to fish for mathematical courses more or less via manual search)
The following links lead to lectures in Russian.
http://bogomolov-lab.ru/SHKOLA/courses.html
a summer school for undergraduates (topics include number theory, metric geometry, anabelian geometry)
http://www.mathnet.ru/php/presentation.phtml?&option_lang=eng 
has a huge collection of videos, including recordings of summer school courses both for undergraduates and graduates.
http://www.lektorium.tv/ is an example of a similar effort.
A: Here is a good series of video lectures from IIT Kharagpur:
https://nptel.ac.in/courses/122104017/ 
A: This collection has a mixture of French and English, but here you can find videos given at the Bicentennial of the Birth of Evariste Galois (Bicentennaire de la naissance d'Evariste Galois) at the Institut Henri Poincaré in Paris.
A: Here you find the videos of the conference "Orbits, Primitive Ideals and Quantum Groups", Weizmann Institute, Israel.
The videos are about:


*

*Finite W-algebras, by I. Losev

*Adapted pairs in a biparabolic subalgebra, by F. Fauquant-Millet

*Hopf Algebra and Root Systems, by H-J Schneider

*Quiver Grassmannians, by M. Reineke

*Quantum quasi-Shuffles, by M. Rosso

A: Steven Miller's ongoing lectures on complex analysis are very stimulating
http://www.youtube.com/channel/UCZ_iaWQx0NpVVKvfT9tuCOg http://web.williams.edu/Mathematics/sjmiller/public_html/
A: Partially orderdered sets course by William T. Trotter: http://posets.tcs.uj.edu.pl/archive/.
A: The Arizona Winter School short course videos have been very helpful. 
A: CIRM has a collection of video courses called CARMIN.TV
A: There are lots of good math courses available here.
A: My lectures on exterior differential systems and the lecture notes.
A: I recently found the YouTube channel of the university of Uppsala (Uppsala Algebra : https://www.youtube.com/channel/UCPWnhR29VHTAk7rZUEDQdDQ/playlists)
It contains mostly courses by Walter Mazorchuk on representation theory of finite groups, Lie algebras and the category O (and on linear algebra which if of less interest for me) and a course on commutative algebra and algebraic geometry by Seidon Alsaody.
I mostly watched the courses by W. Mazorchuk and they are very good.
A: Three courses by Stephen Boyd at Stanford: Introduction to Linear Dynamical Systems, Convex Optimization I, and Convex Optimization II. 
A: Geometric Representation Theory Seminar - Fall 2007 by John Baez and James Dolan

This fall, our seminar is tackling geometric representation theory — the marvelous borderland where geometry, groupoid theory and logic merge into a single subject. The seminar is jointly run by John Baez and James Dolan. Besides explaining well-known stuff, we'll report on research we've done with Todd Trimble over the last few years.

A: This might not fulfill the requirements of being a mathematics course, but I think that it is close enough. In 2006 the Clay Mathematics Institute hosted a Summer School in Arithmetic Geometry. The videos are great if you have a solid foundation in algebraic geometry already and wish to continue in the direction of arithmetic geometry .
A: Coursera  offers not just the videos, but entire courses: I'm currently following Probabilistic Graphical Models, which has weekly exercises and programming projects (which are marked by an autograder), plus community discussion boards and a wiki for collaborating with other students pursuing the course at the same time. Although you could presumably just create an account towards the end of term, archive off all the videos and then watch them at your leisure rather than trying to match the (reasonably demanding) schedule. 
A: David Gay gave a graduate course on Morse Theory at the University of Georgia this spring and the videos are compiled together in a YouTube playlist at Morse Theory: UGA 2012. Notes for his course are also online on the course website.
A: Carmen Rovi's DailyMotion website has 160+ videos on the topology of manifolds in general, and surgery theory in particular, of lectures either given at the University of Edinburgh or at conferences elsewhere. Some of the lectures are courses, and some are one-offs. The November 2012 Edinburgh course of 12 lectures by Rob Kirby on high-dimensional manifold topology is a particular highlight. 
A: Introduction to Algorithms, taught at MIT by Charles Leiserson and Erik Demaine. 
A: Plenty of short courses given at workshops can be found in the Newton Institute archive at newton.cam.ac.uk.
Here is the link: http://www.newton.ac.uk/webseminars/
A: Graduate course on Computational Complexity and Quantum Compuation given at Cambridge University by Timothy Gowers.
A: Multivariable Calculus by Edward Frenkel at Berkeley:
http://www.youtube.com/view_play_list?p=07CF868151394FE3
A: Richard E. Borcherds has posted videos for courses on group theory, commutative algebra, classical Algebraic geometry and scheme theoretic algebraic geometry.
Link
Connecticut summer school in number theory (CTNT) has short courses on different topics, like modular forms, elliptic curves, p-adic numbers, sieve methods, etc.
Link
A: MIT's Open Courseware is a very good source of this http://ocw.mit.edu/index.htm.
I personally recommend the differential equations course they have.   
A: The entire master course at ICTP:
http://www.ictp.tv/diploma/index2.php?activityid=MTH
A: A course on Lie groups taught by Erik van den Ban at Utrecht University.
The parent directory contains a few more bachelor level courses, but these are in Dutch.
A: the link by  Elohemahab Solomon some lectures on lie algebra
A: All Master Classes given at QGM and the previous CTQM are online here: http://qgm.au.dk/video/ and here: http://www.ctqm.au.dk/news/special_events.html.
It is quite an extensive list of 17 Master Classes in total. The courses are on a variety of different subjects, given by among others Maxim Kontsevich, Nicolai Reshetikhin, Nigel Hitchin, Vaughan Jones, Tom Mrowka, Gregor Masbaum, Dylan Thurston, Robert Penner and many more.
A: Here is a good resource of video lectures conducted by IIT's & IISc's:
1
There is also a YouTube channel:
2
A: The courses of the summer school Poisson 2016 (that took place in Geneva) are available online.
The courses are: 


*

*Cohomological methods in field theory: BV, BFV and BRST, by Giovanni Felder
(video: lectures 1 and 2, lecture 3, lecture 4),

*Introduction to Poisson geometry and Lie algebroids by Eckhard Meinrenken
(video: lecture 1, lecture 2, lecture 3, lecture 4)

*Integrable systems, symmetries and quantization by San Vu Ngoc and Daniele Sepe
(video: lecture 1, lecture 2, lecture 3, lecture 4)

*Algebraic methods in holomorphic Poisson geometry by Brent Pym
(video: lecture 1, lecture 2, lecture 3, lecture 4).


Even the lectures of the conference Poisson 2016 (that took place in Zurich) are available online.
A: A one semester introductory course to infinite-dimensional differential geometry (Lie groups and Riemannian geometry) can be found here
A: My course lecture videos:

*

*Introductory linear algebra (44 videos on YouTube, lecture notes in the video descriptions)


*Advanced linear algebra (42 videos on YouTube, lecture notes in the video descriptions)
A: My videos about the application of mathematics in physics are in
https://www.aparat.com/Meisami67
Also there are videos which contain intriguing short questions and their answers.
A: *

*Here are video lectures from Taiwan Mathematics School; some of them were delivered in Mandarin: https://sites.google.com/view/tms-home/media-archive?authuser=0


*The following courses (all in Mandarin) were taught by Professor Chen-Yu Chi at National Taiwan University:



*

*Calculus 1 & Calculus 2. The topics in these courses are more like "advance calculus", not the usual calculus content.

*Analysis 1 & Analysis 2. The topics include complex analysis, de Rham cohomology, functional analysis, Lebesgue integral, smooth manifold, measure theory, ODE, singular homology, topology.

*Algebraic Topology. The main textbook is Algebraic Topology by Edwin H. Spanier.

A: Mini-course on "FROBENIUS MANIFOLDS, IRREGULAR SINGULARITIES, AND
ISOMONODROMY DEFORMATIONS",
The course will consist of 5 lectures, which will be shown live on
YouTube, at the url shown below (where the lectures will stay available
for a later view).
1)Introduction to Frobenius manifolds
2)Examples of Frobenius manifolds
3)Analytic theory of Frobenius manifolds -
I
II
4)Some recent results and work in progress
