The present notes are based on the lectures which I gave at the University of Mannheim from March 1972 to July 1972. The lectures were informal and were Intended to provide an Introduction to the classification theory of higher dimensional algebraic varieties and compact complex spaces recently developed by S. Kawai, S. Iitaka and other mathematicians in Tokyo. The notes were taken by P. Cherenack. Since there were no available lecture notes on these subjects, I decided after reading Cherenack's notes to rewrite them more systematically so that they would serve as an introduction to our classification theory. Several topics which I did not mention at Mannheim have been added.