Preface Chapter I.Combinatorial Games 1.Introduction 2.??CKENBUSH: A Detailed Example 3.How to Read This Book 4.A Survey of the Landscape Chapter II.Short Games 1.The Group G 2.Canonical Form 3.Numbers 4.Infinitesimals 5.Temperature 6.Reduced Canonical Form 7.Atomic Weight Chapter III.The Structure of G 1.Hereditary Structure 2.Lattice Structure 3.Group Structure Chapter IV.Impartial Games 1.Nim Values 2.Heap Games 3.WYTHOFF 4.Generalized Sprague Grundy Theory 5.Nim Arithmetic Chapter V.Mis?re Play 1.Mis?re NIM 2.Genus Theory 3.Mis?re Canonical Form 4.Mis?re Quotients 5.The Structure of Finite Mis?re Quotients 6.Partizan Mis?re Canonical Form Chapter VI.Loopy Games 1.Coping with Cycles 2.Stoppers 3.Simplifcation of Stoppers 4.Sides 5.Idempotents Chapter VII.Temperature Theory 1.Enriched Environments 2.Orthodoxy 3.Generalized Temperature 4.Generalized Thermography 5.Komaster Thermography Chapter VIII.Transfinite Games 1.The Group PG 2.Surreal Numbers 3.The Structure of Surreal Numbers 4.Transfinite Nim Arithmetic Appendix A.Open Problems Appendix B.Mathematical Prerequisites
1.Abelian Groups 2.Partial Orders 3.Ordinals 4.Commutative Semigroups Appendix C.A Finite Loopfree History Bibliography Glossary of Notation Author Index Index of Games Index
[