Introductory Remarks on Computer Algebra -- Basic Notations and Ideas: A Historical Account -- Basic Computational Problems and Their Solution -- An Introduction to SINGULAR -- Practical Session I -- Practical Session II -- Constructive Module Theory and Homological Algebra I -- Homological Algebra II -- Practical Session III -- Solving Systems of Polynomial Equations -- Primary Decomposition and Normalization -- Practical Session IV -- Algorithms for Invariant Theory -- Computing in Local Rings -- Practical Session V.