1 Sets. - 1. Basic Concepts. - 2. Mappings of Sets. - 3. Binary Relations. - 4. Multiplication of Binary Relations. - 2 Algebraic Operations of a General Type. - 1. The Concept of an Algebraic Operation. - 2. Basic Properties of Operations. - 3. Multiplication of Subsets of a Multiplicative Set. - 4. Homomorphisms. - 5. Semigroups. - 6. Elementary Concepts of the Theory of Groups. - 3 Compositions of Transformations. - 1. General Properties of the Composition of Transformations. - 2. Invertible Transformations. - 3. Invertible Transformations of Finite Sets. - 4. Endomorphisms. - 5. Groups of Isometries. - 6. Partial Transformations. - 4 Groups and Their Subgroups. - 1. Decomposition of a Group by a Subgroup. - 2. Conjugate Classes. - 3. Normal Subgroups and Factor Groups. - 4. Subgroups of Finite Groups. - 5. Commutators and the Commutator Subgroup. - 6. Solvable Groups. - 7. Nilpotent Groups. - 8. Automorphisms of Groups. - 9. Transitive Groups of Transformations. - 5 Defining Sets of Relations. - 1. Defining Sets of Relations on Semigroups. - 2. Defining Sets of Relations on Groups. - 3. Free Groups. - 4. Groups Defined by Sets of Relations. - 5. Free Products of Groups. - 6. The Direct Product of Groups. - 6 Abelian Groups. - 1. Elementary Properties of Abelian Groups. - 2. Finite Abelian Groups. - 3. Finitely Generated Abelian Groups. - 4. Infinite Abelian Groups. - 7 Group Representations. - 1. Representations of a General Type. - 2. Representations of Groups by Transformations. - 3. Representations of Groups by Matrices. - 4. Groups of Homomorphisms of Abelian Groups. - 5. Characters of Groups. - 8 Topological and Ordered Groups. - 1. Metric Spaces. - 2. Groups of Continuous Transformations of a Metric Space. - 3. Topological Spaces. - 4. Topological Groups. - 5. Ordered Groups. - Hints. - 1. - 2. - 3. - 4. - 5. - 6. - 7. - 8. - Answers. - 1. - 2. - 3. - 4. - 5. - 6. - 7. - 8. Language: English