Introductory Remarks on Computer Algebra.- 1 Basic Notations and Ideas: A Historical Account.- 2 Basic Computational Problems and Their Solution.- 3 An Introduction to SINGULAR.- Practical Session I .- Practical Session II .- 4 Homological Algebra I .- 5 Homological Algebra II .- Practical Session III .- 6 Solving Systems of Polynomial Equations .- 7 Primary Decomposition and Normalization .- Practical Session .- 8 Algorithms for Invariant .- 9 Computing...