1 Definition and Most Important Subsets of a Group. - 1. Definition of a Group. - 2. Subgroups. Normal Subgroups. - 3. The Center. The Commutator Subgroup. - 2 Homorphisms. - 4. Homomorphisms and Factors. - 5. Endomorphisms. Automorphisms. - 6. Extensions by Means of Automorphisms. - 3 Abelian Groups. - 7. Free Abelian Groups. Rank. - 8. Finitely Generated Abelian Groups. - 9. Divisible Abelian Groups. - 10. Periodic Abelian Groups. - 4 Finite Groups. - 11. Sylow p-Subgroups. - 12. Finite Simple Groups. - 13. Permutation Groups. - 5 Free Groups and Varieties. - 14. Free Groups. - 15. Varieties. - 6 Nilpotent Groups. - 16. General Properties and Examples. - 17. The Most Important Subclasses. - 18. Generalizations of Nilpotency. - 7 Soluble Groups. - 19. General Properties and Examples. - 20. Finite Soluble Groups. - 21. Soluble Matrix Groups. - 22. Generalizations of Solubility. - Append. - Auxiliary Results from Algebra Logic and Number Theory. - 23. On Nilpotent Algebras. - 23. 1. Nilpotence of Associative and Lie Algebras. - 23. 2. Non-Nilpotent Nilalgebras. - 24. Local Theorems of Logic. - 24. 1. Algebraic Systems. - 24. 2. The Language of the Predicate Calculus. - 24. 3. The Local Theorems. - 25. On Algebraic Integers. - Index of Notations for Classical Objects. Language: English