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| Foreword | |
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| Introduction to Topological Groups and Semigroups | |
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| Some algebraic concepts | |
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| Groups and semigroups with topologies | |
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| Neighbourhoods of the identity in topological groups and semigroups | |
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| Open sets, closures, connected sets and compact sets | |
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| Quotients of topological groups | |
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| Products, [Sigma]-products, and [sigma]-products | |
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| Factorization theorems | |
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| Uniformities on topological groups | |
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| Markov's theorem | |
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| Historical comments to Chapter 1 | |
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| Right Topological and Semitopological Groups | |
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| From discrete semigroups to compact semigroups | |
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| Idempotents in compact semigroups | |
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| Joint continuity and continuity of the inverse in semitopological groups | |
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| Pseudocompact semitopological groups | |
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| Cancellative topological semigroups | |
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| Historical comments to Chapter 2 | |
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| Topological groups: Basic constructions | |
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| Locally compact topological groups | |
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| Quotients with respect to locally compact subgroups | |
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| Prenorms on topological groups, metrization | |
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| [omega]-narrow and [omega]-balanced topological groups | |
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| Groups of isometries and groups of homeomorphisms | |
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| Raikov completion of a topological group | |
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| Precompact groups and precompact sets | |
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| Embeddings into connected, locally connected groups | |
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| Historical comments to Chapter 3 | |
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| Some Special Classes of Topological Groups | |
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| Ivanovskij-Kuz'minov Theorem | |
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| Embedding D[superscript omega 1] in a non-metrizable compact group | |
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| Cech-complete and feathered topological groups | |
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| P-groups | |
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| Extremally disconnected topological and quasitopological groups | |
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| Perfect mappings and topological groups | |
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| Some convergence phenomena in topological groups | |
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| Historical comments to Chapter 4 | |
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| Cardinal Invariants of Topological Groups | |
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| More on embeddings in products of topological groups | |
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| Some basic cardinal invariants of topological groups | |
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| Lindelof [Sigma]-groups and Nagami number | |
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| Cellularity and weak precalibres | |
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| o-tightness in topological groups | |
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| Steady and stable topological groups | |
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| Cardinal invariants in paratopological and semitopological groups | |
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| Historical comments to Chapter 5 | |
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| Moscow Topological Groups and Completions of Groups | |
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| Moscow spaces and C-embeddings | |
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| Moscow spaces, P-spaces, and extremal disconnectedness | |
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| Products and mappings of Moscow spaces | |
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| The breadth of the class of Moscow groups | |
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| When the Dieudonne completion of a topological group is a group? | |
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| Pseudocompact groups and their completions | |
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| Moscow groups and the formula v(X x Y) = vX x vY | |
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| Subgroups of Moscow groups | |
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| Pointwise pseudocompact and feathered groups | |
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| Bounded and C-compact sets | |
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| Historical comments to Chapter 6 | |
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| Free Topological Groups | |
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| Definition and basic properties | |
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| Extending pseudometrics from X to F(X) | |
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| Extension of metrizable groups by compact groups | |
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| Direct limit property and completeness | |
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| Precompact and bounded sets in free groups | |
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| Free topological groups on metrizable spaces | |
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| Nummela-Pestov theorem | |
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| The direct limit property and countable compactness | |
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| Completeness of free Abelian topological groups | |
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| M-equivalent spaces | |
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| Historical comments to Chapter 7 | |
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| R-Factorizable Topological Groups | |
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| Basic properties | |
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| Subgroups of R-factorizable groups. Embeddings | |
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| Dieudonne completion of R-factorizable groups | |
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| Homomorphic images of R-factorizable groups | |
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| Products with a compact factor and m-factorizability | |
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| R-factorizability of P-groups | |
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| Factorizable groups and projectively Moscow groups | |
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| Zero-dimensionality of R-factorizable groups | |
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| Historical comments to Chapter 8 | |
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| Compactness and its Generalizations in Topological Groups | |
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| Krein-Milman Theorem | |
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| Gel'fand-Mazur Theorem | |
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| Invariant integral on a compact group | |
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| Existence of non-trivial continuous characters on compact Abelian groups | |
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| Pontryagin-van Kampen duality theory for discrete and for compact groups | |
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| Some applications of Pontryagin-van Kampen's duality | |
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| Non-trivial characters on locally compact Abelian groups | |
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| Varopoulos' theorem: the Abelian case | |
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| Bohr topology on discrete Abelian groups | |
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| Bounded sets in extensions of groups | |
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| Pseudocompact group topologies on Abelian groups | |
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| Countably compact topologies on Abelian groups | |
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| Historical comments to Chapter 9 | |
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| Actions of Topological Groups on Topological Spaces | |
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| Dugundji spaces and 0-soft mappings | |
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| Continuous action of topological groups on spaces | |
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| Uspenskij's theorem on continuous transitive actions of [omega]-narrow groups on compacta | |
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| Continuous actions of compact groups and some classes of spaces | |
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| Historical comments to Chapter 10 | |
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| Bibliography | |
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| List of symbols | |
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| Author Index | |
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| Subject Index | |