The second volume of this comprehensive treatise focusses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation here is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in issues of implementation. Aiming to be a complete survey on Groebner bases and their applications, the book will be essential for all workers in commutative algebra, computational algebra and algebraic geometry.