These lectures represent a condensation of a number of colloquia, seminars and discussions held at the Institute of Theoretical Physics of the University of Graz during the last years and epitomize the principal lines of research undertaken by my group. From the very beginning of my appointment at the University of Graz in 1947 I have been concerned with the task of bringing up a relatively small group of scientifically interested and open-minded co-workers and of stimulating them to sound scientific research. Since 1930 I myself have dealt with subjects of the kind treated in these lectures, to which I was introduced by my late friend and teacher TH. SEXL. But also as assistant and co-worker of E. FUES and R. THIRRING I frequently worked on these problems, constantly using new methods and lines of approach. During the last years of the war and the first ones afterwards Ihad the fortunate opportunity to receive many stimulating ideas and comments on my work from A. SOMMERFELD on the occasion of my frequent visits to Munich. Especially this last period, although partially connected with personal difficulties and troubles of many kinds stemming from the turbulence of lost-war readjustments, I consider to be one of the most valuable times in my life.