Are there detailed expositions of the path integral methods in (mathematical) physics other than FeynmanHibbs and GlimmJaffe?

4$\begingroup$ There are several references contained in answers to relevant questions here on MO, for example mathoverflow.net/questions/19495/… or mathoverflow.net/questions/24823/… $\endgroup$– მამუკა ჯიბლაძეDec 19, 2015 at 17:33
3 Answers
Hagen Kleinert
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets
http://users.physik.fuberlin.de/~kleinert/kleinert/?p=loadbook&book=8
that book seems most comprehensive
Of course the physics literature is full of references on path integrals. One would not know where to start. Kleinert's books suggested by Alexander must be a good choice. On the rigorous side you might want to have a look at:
"Functional Integration and Quantum Physics" by Barry Simon, Academic Press 1979.
"FeynmanKacType Theorems and Gibbs Measures on Path Space" by Lorinczi, Hiroshima and Betz, De Gruyter 2011.

1$\begingroup$ Just to briefly indicate that there is a second edition of Simon's book (AMS Chelsea, 2004). $\endgroup$ Feb 22, 2016 at 16:26
An impressive list of references to complement the answers already given can be found at the bottom of the following Scholarpedia article by Sergio Albeverio and Sonia Mazzucchi. The approach to path integrals based on "cylindrical measures", aka "promeasures", is not discussed in the body of the article but can be read about in the work by DeWittMorette and collaborators referenced there.