Theory of Group Representations

I Algebraic Foundations of Representation Theory.- x1. Fundamental Concepts of Group Theory.- x2. Fundamental Concepts and the Simplest Propositions of Representation Theory.- II Representations of Finite Groups.- x1. Basic Propositions of the Theory of Representations of Finite Groups.- x2. The Group Algebra of a Finite Group.- x3. Representations of the Symmetric Group.- x4. Induced Representations.- x5. Representations of the Group SL (2, Fq).- III Basic Concepts of the Theory of Representations of Topological Groups.- x1. Topological Spaces.- x2. Topological Groups.- x3. Definition of a Finite-Dimensional Representation of a Topological Group; Examples.- x4. General Definition of a Representation of a Topological Group.- IV Representations of Compact Groups.- x1. Compact Topological Groups.- x2. Representations of Compact Groups.- x3. The Group Algebra of a Compact Group.- V Finite-Dimensional Representations of Connected Solvable Groups; the Theorem of Lie.- x1. Connected Topological Groups.- x2. Solvable and Nilpotent Groups.- x3. Lie's Theorem.- VI Finite-Dimensional Representations of the Full Linear Group.- x1. Some Subgroups of the Group G.- x2. Description of the Irreducible Finite-Dimensional Representations of the Group GL (n, C).- x3. Decomposition of a Finite-Dimensional Representation of the Group GL(n, C) into Irreducible Representations.- VII Finite-Dimensional Representations of the Complex Classical Groups.- x1. The Complex Classical Groups.- x2. Finite-Dimensional Continuous Representations of the Complex Classical Groups.- VIII Covering Spaces and Simply Connected Groups.- x1. Covering Spaces.- x2. Simply Connected Spaces and the Principle of Monodromy.- x3. Covering Groups.- x4. Simple Connectedness of Certain Groups.- IX Basic Concepts of Lie Groups and Lie Algebras.- x1. Analytic Manifolds.- x2. Lie Algebras.- x3. Lie Groups.- X Lie Algebras.- x1. Some Definitions.- x2. Representations of Nilpotent and Solvable Lie Algebras.- x3. Radicals of a Lie Algebra.- x4. The Theory of Replicas.- x5. The Killing Form; Criteria for Solvability and Semisimplicity of a Lie Algebra.- x6. The Universal Enveloping Algebra of a Lie Algebra.- x7. Semisimple Lie Algebras.- x8. Cartan Subalgebras.- x9. The Structure of Semisimple Lie Algebras.- x10. Classification of Simple Lie Algebras.- x11. The Weyl Group of a Semisimple Lie Algebra.- x12. Linear Representations of Semisimple Complex Lie Algebras.- x13. Characters of Finite-Dimensional Irreducible Representations of a Semisimple Lie Algebra.- x14. Real Forms of Semisimple Complex Lie Algebras.- x15. General Theorems on Lie Algebras.- XI Lie Groups.- x1. The Campbell-Hausdorff Formula.- x2. Cartan's Theorem.- x3. Lie's Third Theorem.- x4. Some Properties of Lie Groups in the Large.- x5. Gauss's Decomposition.- x6. Iwasawa's Decomposition.- x7. The Universal Covering Group of a Semisimple Compact Lie Group.- x8. Complex Semisimple Lie Groups and Their Real Forms.- XII Finite-Dimensional Irreducible Representations of Semisimple Lie Groups.- x1. Representations of Complex Semisimple Lie Groups.- x2. Representations of Real Semisimple Lie Groups.- A: Monographs and Textbooks.- B: Journal Articles.