Parts I-III of the book provide relatively elementary material about representation theory on finite groups and on compact Lie groups. A chapter on simple groups of the Lie type has been added to the original notes so that the reader can have a complete picture of simple finite groups. Part IV presents some advanced material on infinite-dimensional representations of non-compact groups. The last part of the notes touches on many important ideas of current research, such as orbit methods, minimal representations and dual pair correspondences, which may serve as an introduction to the current research on representation theory.