Non-Commutative Geometry Methods for Group C*-Algebras

This research notes is intended to provide a quick introduction to the subject. We expose a K-theoretic approach to study group C*-algebras: started in the elementary part, with one example of description of the structure of C*-algebras of the group of affine transformations of the real straight line, continued then for special classes of solvable and nilpotent Lie groups. In the second advanced part, we introduced the main tools of the theory. In particular, the conception of multidimensional geometric quantization and the index of group C*-algebras were created and developed.