A reading list for topological quantum field theory? Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic algebraic topology, and have some basic background in quantum field theory.
Perhaps others with different backgrounds will also be interested in a reading list on TQFTs, so feel free to ignore my background and suggest material at a variety of levels.
 A: I've found the following articles useful in the past:
Segal's notes: http://www.cgtp.duke.edu/ITP99/segal/
Atiyah's paper "Topological quantum field theories"
A: If you want something from a more QFT point of view, Witten's 1989 paper on the Jones polynomial is pretty readable.
Link
A: I once tried myself on collecting a reading list, or at least a reference list at 
nLab:FQFT 
("FQFT" for "Functorial QFT" as opposed to other formalization approaches like "algebraic" QFT, which have not been applied that much to the topological case). 
This also points to more introductory stuff by John Baez, if that's a selling point, namely to his article "Quantum quandaries" with is one of the best expositions for why that idea of representations of cobordisms categories is a good one in the first place.
But it also contains links to (some of) the historical articles and then to those describing further development, trying to put it all in a big picture.
A: This recent paper of 2016 contains a useful introduction to the new development in TQFT for strongly coupled condensed matter system and topological quantum matter in 3-dimensions, 4-dimensions and any dimension. 
The authors point out the relations between quantum Hamiltonian lattice models, the continuum TQFTs and group cohomology/cobordism theory.
https://arxiv.org/abs/1612.09298
Annals of Physics 384C, 254-287 (2017)
DOI: 10.1016/j.aop.2017.06.019

A: Try This Week's Finds in Mathematical Physics first. It has some classic references, e.g. Atiyah's book:

The Geometry and Physics of Knots, by Michael Atiyah, Cambridge U. Press, 1990.

(update: Atiyah has many books and to my knowledge any of them is worth a look)
A: You might also be interested in new "fermionic" theories, with new and almost totally unexplored features. If yes, see e.g. arXiv:0907.3787 and arXiv:0911.1395. To understand these properly, you should read, however, at least something in the beginning of Turaev's book on torsions (but not his papers on quantum invariants) and, of course, some book on Grassmann-Berezin calculus of anticommuting variables (a few relevant pages in Berezin's book on Second Quantization will work).
A: A recent addition is provided by the recent text Topological Field Theory, Higher Categories, and Their Applications  of Anton Kapustin
A: This might be a little too simple/review-like for someone with your background, but it is a cute little article and might be a nice introduction: http://arxiv.org/abs/0810.0344
A: There is a new book available, Dirichlet Branes and Mirror Symmetry, written by both mathematicians and physicists. It contains a chapter on TQFT written by Moore and Segal which is based on this paper. This book is supposed to be written such that mathematicians are able to understand it, and I think that the authors achieved this goal.
A: I found Bruce Bartlett's MSc dissertation Categorical Aspects of Topological Quantum Field Theories a very clear and well-written introduction to TQFTs and related matters.
A: I think it might be worth pointing out that there are two kinds of topological quantum field theory, (Albert) Schwarz-type theories and Witten-type theories.  In Schwarz type theories (like Chern-Simons theory and BF-theory), you have an action which is explicitly independent of the metric and you expect that the correlation functions computed by the path integral will also be independent of the metric.  In Witten-type theories (Donaldson theory, Gromov-Witten theory), metric independence is a little bit more subtle.  In these theories, you do have to choose a metric to get started.  But you have some extra structure that allows you to compute some quantities which are metric independent.
(Slightly) more precisely:  In a Witten-type theory, you have some operator Q which squares to zero, which you think of as a differential.   (Witten type theories are also called cohomological field theories.)  You also have an operator T, taking values in (2,0)-tensors, which a) is Q-exact ( T = [Q,G] for some G), and b) generates changes in the metric g.  The latter means that if we compute the expectation value < epsilon(T)A > as a function of g, we find that it's equal to the expectation value of A computed with respect to g + epsilon.  Here epsilon is a "small" (0,2) tensor we pair with T to get a scalar.  In these theories, you can show that the correlation functions of operators which are Q-exact must vanish, which implies that small deformations of g don't change the correlation functions of Q-closed operators A.  If you choose A so that its expectation value behaves like a function on the space of metrics, this tells you it's constant on the space of metrics.  If you choose some fancier A so that the correlation functions behave like differential forms on the space of metrics, cohomological complications can arise.
Most of the references here are for Schwarz-type theories.  For a physics treatment of  Witten-type theories, it's worth looking at Witten's "Introduction to cohomological field theory".  There's also a long set of lecture notes by Cordes, Moore, & Ramgoolam.  The mathematical treatments of the idea are less complete.  Hopkins, Lurie, & Costello's stuff is about the most comprehensive, but it's pretty far removed from actions and path integrals.  For a starter, you might enjoy Teleman's classification of 2d semi-simple "families topological field theories".
A: There is a very accessible book by Joachim Kock, "Frobenius Algebras and 2D Topological Quantum Field Theories"
A: There's a nice overview of many of the "higher categorical issues" in John Baez's paper Higher dimensional algebra and TQFT. It's also very friendly for beginners.
For the details, from a perspective emphasising the 2- and 3-categories that make everything tick, you should read


*

*Bakalov-Kirillov

*Turaev's big blue book


Dan Freed's paper are also very good. For a somewhat different perspective, try Kevin Walker's TQFT notes, on his webpage.
A: Some new developments relating TQFTs and Morse theory by Losev, Frenkel and Nekrasov
hep-th/0610149
arXiv:0803.3302
