This book provides a unique introduction to the theory of point processes by one of the founding fathers of the subject. It is the translation of a course in French given by Prof. Klaus Krickeberg in the academic year 1976/77 at the Mathematics Department of the University Paris Sud (Orsay). Several scholia by Prof. Hans Zessin describe shortly certain developments which took place in the last four decades. The text forms an excellent introduction for graduate students and postgraduates. They will gain a broad and deep understanding of the foundations of the theory as well its applications.