A good book of functional analysis I'm a student (I've been studying mathematics 4 years at the university) and I like functional analysis and topology, but I only studied 6 credits of functional analysis and 7 in topology (the basics). What I am looking for is good books that I could understand to go deeper in this areas, what do you recommend? (I can read in Spanish, English, French and German)
 A: When I was studying, I was influenced much by K. Yosida's "Functional Analysis".
A: I'd recommend the Dunford and Schwartz. It's a classic. It's huge -- three volumes. But you don't have to read the whole series cover-to-cover. If you read half of the first volume, you'll learn about as much as reading many other books on functional analysis. Volume 1 alone is big, but it's easy to read for a book on its subject.
A: Apart from the classics already mentioned (Yosida, Brezis, Rudin), a good book of functional analysis that I think is suitable not only as a reference but also for self-study, is Fabian, Habala et al. Functional Analysis and Infinite-Dimensional Geometry. It has a lot of nice exercises, it's less abstract than the usual book and provides a lot of "concrete" theorems.
And I'm not sure about it, but I heard there is a spanish translation (the original is of course in english).
A: I personally like a recent book of Helemskii Lectures and Exercises on Functional Analysis. One of the differences with other books on the subject is that it uses the categorical
point of view. The author starts with a very brief introduction to the category theory and uses this language throughout the book. It's a sort of modern core of FA book, with a sidelines to some physics applications and of historic nature, a terse advertisement of the quantum functional analysis and so on (but there is no measure theory, Radon Nikodym theorem etc. which are elaborated in many excellent old textbooks.) Also it gives somewhat broader picture of FA sketching some directions and stating from time to time theorems without proofs 'that every student should know'.
A: I am an algebraist and not an analyst, however my favourite book on this area is "Walter Rudin: Functional Analysis".
A: The book on Functional Analysis by Meise and Vogt 
http://books.google.de/books?id=FavCGyUirRkC&dq=Meise+Vogt&hl=de&ei=F1JBTpPXItOx8QOdtPm4CQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDEQ6AEwAQ
is quite comphrensive and contains beside standard functional analysis more advanced sections on the theory of locally convex spaces. There is also a German version if you want to improve your German by reading both together.
A: Zimmer's Essential Results of Functional Analysis is a very interesting read, specially if you already know some basic stuff in functional analysis.
A: I am not an analyst of any sort, so you do not need to listen to me, but I really like Lax's "Functional Analysis".
A: My preferred text(s) for functional analysis are
(1) B.V. Limaye, Functional Analysis
(2) P.D. Lax, Functional Analysis
(3) R. Larsen, Functional Analysis
Book by Larsen introduces seminormed linear spaces, which in my opinion has enough generali
A: I have learnt Functional Analysis from Peter Lax himself. His book is his notes. Exactly the same notes as the ones he handed to us. Every chapter consists of one two-hours long lecture in a two semester graduate course on Functional Analysis. There are a few mistakes here and there, but this book is really ALIVE! It is as if you are in a class of Peter Lax! (I should note here that, Lax's book is published a long time after I left Courant, and at that time the recommended textbook was Yosida's book together with Dunford & Schwartz.)
Having said all these, I should add that as an undergraduate student, I had taken two semesters of Functional Analysis which covered a part of Rudin's book. I still use this book sometimes, as some topics are presented in a beautiful way, but I believe that it is far from introductory, as it starts with Topological Vector Spaces, and it takes a while before normed spaces are mentioned.
A: I would suggest the book by Haim Brezis: Analyse fonctionnelle, theorie et applications. It was recently translated into English and you can find the information for the English translation here.
A: Some of the good books are:


*

*Elements of the Theory of Functions and Functional Analysis by Kolmogorov, Fomin.


*Functional Analysis, by F.Riesz and Nagy.


*Functional Analysis : Spectral Theory by V.Sunder. Freely available here.


*Analysis now. By Gert Kjeargård Pedersen. (As suggested by Theo Buehler at $\textbf{Math.SE}$


*Stein, Elias; Shakarchi, R. (2011). Functional Analysis: An Introduction to Further Topics in Analysis. Princeton University Press. ISBN 0691113874.


*Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext) by Haim Brezis.


*Elementary Functional Analysis by Georgi E. Shilov.


*Introductory Functional Analysis with Applications by Erwin Kreyszig.


*Notes on Functional Analysis by Rajendra Bhatia. (Hindustan Book Agency.)


*Functional Analysis by S.Kesavan. ( Hindustan Book Agency.)


*Elementary functional analysis By Barbara D. MacCluer


*Functional analysis: an introduction By Yuli Eidelman, Vitali D. Milman, Antonis Tsolomitis (AMS)


*Principles of functional analysis By Martin Schechter. (AMS)


*You may also want to see this thread: Problem books in Functional Analysis


$\textbf{Note.}$ The books which are written in Italics are the ones which I have read partially. The ones which are not in Italics are the ones which I have come to know (by friends, teachers) are good books in Functional Analysis.  Also, I really don't know which publisher actually publishes the book in foreign edition written by Kesavan and Bhatia.
A: You might be interested in "Analysis Now" by Pedersen. A very nice book on graduate level analysis in my opinion. It covers some areas of functional analysis as well.
A: In a course I'm taking now, we're using Gerald Teschl's "Topics in Real and Functional Analysis". It seems like you may already know the first few chapters, however. 
It's quite well written, and is free: http://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html 
A: The Book "Funktionalanalysis: Theorie und Anwendung" from Harro Heuser gives you a very good introduction as well. 
A: I second Reed and Simon's methods of mathematical physics. However, if you are interested primarily in the applications of functional analysis to PDE, for the most part a couple of appendices of Evans' book suffice in my opinion.
A: Since you read German, my favorite is Funktionalanalysis by Dirk Werner.  It's not necessarily comprehensive, but it covers a lot, has extensive historical remarks, and is extremely well-written -- I find it more readable than most math books in English (my first language).
A: John B. Conway's "A course in functional analysis" is also pretty decent.
A: There's no reason to listen to me either, but for delving a bit deeper, you might want to check out T. W. Körner's Fourier Analysis.  The book consists of very short (often just a couple of pages) chapters which contain gems like computing the age of the Earth.  
A: Let me add to this list of suggestions the nice and recent book by J. Cerda "Linear Functional Analysis", Graduate Studies in Mathematics, Vol. 116, AMS-RSME, 2010. 
A: I found Principles of Functional Analysis By Martin Schechter and Functional Analysis By Bachman and Narici to be good introductions to the subject.
A: The best book, I have read it in the past, that I think (I'm not a professor) fits this need is the book in Spanish by Antonio Aizpuru Tomás from Universidad de Cádiz with title  Apuntes incompletos de análisis funcional, Editorial UCA (2009).
