This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling.

The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel, Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.

Contents:

• Quadratic Equations (Rings)
• Curves and Surfaces (Fields)
• Tangents and Polars (Valuations)
• Varieties and Models (Ideals)
• Projective Varieties (Modules)
• Pause and Refresh (Groups)

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Readership: Students and lecturers in mathematics, computer science and engineering.

"I cannot imagine that any mathematician would read even a few pages of this book without learning something new or seeing a new connection or gaining an insight into something that they thought they already knew. And between those insights and his writing, you will soon find yourself captivated by Abhyankar as well. I recommend that anyone with an interest in algebra find a copy of this book and flip through it."