Introduction to commutative algebra sole aim to lead the further stage in the computational revolution in commutative algebra? ? system makes it one of the most flexible and most efficient of the kind .... Another strength of Greuel and Pfister book is the breadth of coverage of theoretical topics in a part of commutative algebra closest to algebraic geometry, with algorithmic treatments almost every topic .... Greuel and Pfister have written a unique and extremely useful book which should be in the library every commutative algebra and algebraic geometry, the same experts and beginners. "Little, MAA, March 2004 The second edition is substantially enlarged by a chapter on Groebner bases in non-commtative ring, a chapter on the set of characteristics and triangles with applications for primary decomposition and polynomial-solving and appendix on polynomial factorization including factorization over algebraic extension field factorization and absolute, in the case of uni- and multivariate.