The author of this book is well known in algebraic geometry, and, as of late in the field of computer graphics. In this book, he summarizes beautifully various results in algebraic geometry that were known at the time of publication. Most importantly, the author believes that in order to properly understand algebraic geometry, one must delve into the works of `Italian' algebraic geometry, as well as the works of Zariski, Weil, and Grothendieck. The former assists in building intuition, while the latter gives a unified algebraic framework in which to work in and relates the subject to number theory. Every student of algebraic geometry has perhaps been overwhelmed by the sheer volume of results in the subject, and the increasing level of abstraction in the form of the theory of schemes, that is encountered when learning algebraic geometry. This book introduces the `classical' point of view, with the modern scheme-theoretic approach left to a future work, says the author. Since its publication, many new interesting approaches have been taken toward algebraic geometry, one being that use is being made of the computer and various symbolic programming languages in order to deal with the geometric objects from a computational point of view. Another has been the role of physics, particularly that of `mirror symmetry' and superstring and M-theory. In fact, one might expand the words of the author in the introduction to this book, and now say that a proper understanding of algebraic geometry should also involve an understanding of quantum field theory, integrable systems, and superstring and membrane theory.