Vladimir Kanovei 
Borel Equivalence Relations [PDF ebook] 

Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications. This book should be of interest to a wide spectrum of mathematicians working in set theory as well as the other areas mentioned. It provides a systematic exposition of results that so far have been only available in journals or are even unpublished. The book presents unified and in some cases significantly streamlined proofs of several difficult results, especially dichotomy theorems. It has rather minimal overlap with other books published in this subject.