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Computational Algebraic Geometry (CAG) is a well-defined collection of the algebra of polynomial ideals, the geometry of affine varieties and wonderful implementations of algorithms. It describes algebraic geometry as a practical and experimental subject. CAG is mainly based on the development of Groebner Basis and the Buchberger Algorithm. A big contribution to the development of Groebner Basis was due to the implementation of the Buchberger Algorithm on the computer algebra systems Axiom, Cocoa, Mathematica, Maple, Macaulay, Reduce, etc. As an introduction to CAG, in this book we study some common questions in affine varieties and we show that computational techniques are much more informative and motivating than theoretical point of view.