1.Lie Algebras. 2.Topological groups. 3.Lie groups. 4.Homogeneous and symmetric spaces. 5.Group representations. 6.Representations of commutative groups. 7.Representations of compact groups. 8.Finite-dimensional representations of Lie groups. 9.Tensor operators, enveloping algebras and enveloping fields. 10.The explicit construction of finite-Dimensional irreducible. 11.Representation theory of Lie and enveloping algebras by unbounded operators: analytic vectors and intregrability. 12.Quantum dynamical applications of Lie algebra representation. 13.Group theory and group representation in quantum theory. 14.Harmonic analysis on Lie groups. Special functions and group representations. 15.Harmonic analysis on homogeneous spaces. 16.Induced representations. 17.Induced representations of semidirect products. 18.Fundamental theorems of semisimple Lie groups. 19.Induced representations of semisimple Lie groups. 20.Application of induced representations. 21.Group representations in relativistic quantum theory.