As the primary tool for doing explicit computations in polynomial rings in many variables, Gr?bner bases are an important component of all computer algebra systems. They are also important in computational commutative algebra and algebraic geometry. This book provides a leisurely and fairly comprehensive introduction to Gr?bner bases and their applications. Adams and Loustaunau cover the following topics: the theory and construction of Gr?bner bases for polynomials with coefficients in a field, applications of Gr?bner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and Gr?bner bases in modules, and the theory of Gr?bner bases for polynomials with coefficients in rings. With over 120 worked out examples and 200 exercises, this book is aimed at advanced undergraduate and graduate students. It would be suitable as a supplement to a course in commutative algebra or as a textbook for a course in computer algebra or computational commutative algebra. This book would also be appropriate for students of computer science and engineering who have some acquaintance with modern algebra.