This book has almost 800 pages with 10 chapters, 3 indexes and 549 items in the bibliography. There are many deep results on generalizations of topological groups (like right, semitopological, quasitopological or paratopological ones, as well as semigroups) and even more and deeper results on special classes of topological groups (e.g. compact, free and R-factorizable). The book can be interesting both for beginners (the explanation starts slowly with elementary facts) and for experts in the field. All classical and recent results are included with proofs (which are sometimes new). In addition to classical information, there are chapters on cardinal invariants on topological groups, Moscow topological groups, completions of groups, free topological groups, R-factorizable groups and actions of topological groups on topological spaces. About 90 sections contain exercises and problems, many sections contain open problems and every chapter contains historical remarks. It is a very useful and valuable book.