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.