chapter 1 Preliminaries -- chapter 2 Polish Groups -- chapter 3 Polish Group Actions -- chapter 4 Finer Polish Topologies -- part Part II: Theory of Equivalence Relations -- chapter 5 Borel Reducibility -- chapter 6 The Glimm–Effros Dichotomy -- chapter 7 Countable Borel Equivalence Relations -- chapter 8 Borel Equivalence Relations -- chapter 9 Analytic Equivalence Relations -- chapter 10 Turbulent Actions of Polish Groups -- part Part III: Countable Model Theory -- chapter 11 Polish Topologies of Infinitary Logic -- chapter 12 The Scott Analysis -- chapter 13 Natural Classes of Countable Models -- part Part IV: Applications to Classification Problems -- chapter 14 Classification by Example: Polish Metric Spaces -- chapter 15 Summary of Benchmark Equivalence Relations.