This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a onesemester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry. Readership Advanced undergraduates, graduate students, and research mathematicians interested in algebra and algebraic geometry; those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry. Reviews "The present small book offers a nice introduction to algebraic geometry, based on an elementary algebraic level, without the use of sheaf or cohomology theory. ...The book is nicely written and can be recommended to anybody interested in basic algebraic geometry."  EMS Newsletter "The book balances theory and examples well and the exercises are wellchosen to further illustrate the basic concepts. All in all, the book does an excellent job of explaining what algebraic geometry is about, what are the basic results, and it invites the reader to continue exploring the subject ... I would definitely recommend it as reading material to a bright undergraduate who has taken a basic course on rings and fields and has read about Noetherian rings. It is certainly suitable for a onesemester graduate course ... Mathematicians from other areas will also enjoy the book ... [It] reminds me of more oldfashioned books on algebraic geometry ... but updated to our modern standards of rigor and shorter attention span."  MAA Online From a review for the German Edition: "The introduction contains numerous examples which illustrate and motivate the discussed theory and which reappear, as the course develops, handled in a precise and clear manner ... Each section ends with interesting and doable (!) exercises ... the author makes a great effort to prove most of the theorems in the rigorous way ... Precision and clarity are distinguished features of the reviewed test."  MathSciNet, Mathematical Reviews on the Web "The book remains one of the very best introductory texts on algebraic geometry. The last chapter is a masterpiece of didactic art ... absolutely unique for such an elementary textbook."  Zentralblatt MATH Table of Contents  Introduction
 Affine varieties
 Projective varieties
 Smooth points and dimension
 Plane cubic curves
 Cubic surfaces
 Introduction to the theory of curves
 Bibliography
 Index
