This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particul

This book contains eight papers on representations and cohomology of Lie algebras. The Lie algebras here are either infinite-dimensional, are defined over field

(Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algeb

Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theo