This book starts by recalling some facts from descriptive set theory. After a chapter on Borel ideals and an introduction to equivalence relations, the author presents material on countable equivalence relations, hyperfinite equivalence relations, dichotomy theorems, actions of the infinite symmetric group and turbulent group actions. Besides other topics, the author further discusses c0-equalities, pinned equivalence relations and reduction of Borel equivalence relations to Borel ideals. The book ends with an appendix on Cohen and Gandy-Harrington forcing. Methods of forcing are used in many places as well as methods of effective descriptive set theory. Many recent results and open problems are included. This is a very interesting book covering many topics of the theory of Borel equivalence relations.