This book is based on a lecture course that I gave at
the University of Regensburg. The purpose of these lectures
was to explain the role of Kahler differential forms in
ring theory, to prepare the road for their application in
algebraic geometry, and to lead up to some research problems
The text discusses almost exclusively local questions and
is therefore written in the language of commutative alge-
algebra. The translation into the language of algebraic geometry
is easy for the reader who is familiar with sheaf theory
and the theory of schemes.