As algebra becomes more widely used in a variety of applications and computers are developed to allow efficient calculations in the field, so there becomes a need for new techniques to further this area of research. Gr?bner Bases is one topic which has recently become a very popular and important area of modern algebra. This book provides a concrete introduction to commutative algebra through Gr?bner Bases. The inclusion of exercises, lists of further reading and related literature make this a practical approach to introducing Gr?bner Bases. The author presents new concepts and results of recent research in the area allowing students and researchers in technology, computer science and mathematics to gain a basic understanding of the technique. A first course in algebra is the only prior knowledge required for this introduction. Chapter titles include: Monomial ldeas Gr?bner Bases Algebraic Sets Solving Systems of Polynomial Equations Applications of Gr?bner Bases Homogeneous Algebra Hilbert Series Variations of Gr?bner Bases Improvements to Buchberger's Algorithms Software