Geometry, Algebra, and Algorithms.- Groebner Bases.- Elimination Theory.- The Algebra-Geometry Dictionary.- Polynomial and Rational Functions on a Variety.- Robotics and Automatic Geometric Theorem Proving.- Invariant Theory of Finite Groups.- Projective Algebraic Geometry.- The Dimension of a Variety.
From the reviews of the third edition: "The book gives an introduction to Buchberger's algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations, and elimination theory. ... The book is well-written. ... The reviewer is sure that it will be a excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry." (Peter Schenzel, Zentralblatt MATH, Vol. 1118 (20), 2007)
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