Lie Groups and Quantum Mechanics

These notes are based on a series of twelve lectures given at the University of Bonn in the Wintersemester 1966-67 to a mixed group of mathematicians and theoretical physicists. I am grateful to Professors H~rzebruch, Bleuler and Klingenberg for giving me the opportunity of speak~at their seminar.
These notes are written primarily for the mathematicianwho has an elementary acquaintance with Lie groups and Lie algebras and who would like an account of the ideas which arise from the concept of relativistic invariance in ouantum mechanics. They may also be of interest to the theoretical physicist who wants to see familiar material presented in a fo~which uses standard concepts from other I areas of mathematics.