This book aims to lead to a further stage in the computational revolution in commutative algebra. It is the first handbook/tutorial extensively dealing with SINGULAR. Among the great strengths and most distinctive features is a new, completely unified treatment of the global and local theories. Another strength of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic. The authors have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike.

This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book's most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

Rings, Ideals and Standard Bases.- Modules.- Noether Normalization and Applications.- Primary Decomposition and Related Topics.- Hilbert Function and Dimension.- Complete Local Rings.- Homological Algebra.