These notes were prepared for the DMV-Seminar held in Dusseldorf, Schloss Mickeln from June 28 to July 5, 1987. They consist of two parts which can be read independently. The reader is presumed to have a basic education in differential and algebraic topology. Surgery theory is the basic tool for the investigation of differential and topological manifolds. A systematic development of the theory is a long and difficult task. The purpose of these notes is to describe simple examples and at the same time to give an introduction to some of the systematic parts of the theory. The first part is...