A complete survey of Grö, bner bases and their applications, this book will be essential for all workers in commutative algebra, computational algebra and algebraic geometry. The second volume of the treatise focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation is based on the intrinsic linear algebra structure of Grö, bner bases, making this a state-of-the-art reference on issues of implementation.