This book can be understood as a model for teaching commutative algebra, taking into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the text shows how to handle it by computer. The computations are exemplified with the computer algebra system SINGULAR developed by the authors. SINGULAR is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry.
The book includes a CD with a version of SINGULAR for various platforms (Unix/Linux, Windows, Macintosh), including all examples and procedures explained in the book. The book can be used for courses, seminars and as a basis for studying research papers in commutative algebra, computer algebra and algebraic geometry.

• Rings, Ideals and Standard Bases
• Modules
• Noether Normalization and Applications
• Primary Decomposition and Related Topics
• Hilbert Function
• Complete Local Rings
• Homological Algebra
• Appendix A. Geometric Background
• Appendix B. SINGULAR - A Short Introduction
• B. SINGULAR Reference Manual
• Index
• Glossary.