Algebraic Geometry has been at the center of much of mathematics
for hundreds of years. It is not an easy field to break into,
despite its humble beginnings in the study of circles, ellipses,
hyperbolas, and parabolas. This text consists of a series of
exercises, plus some background information and explanations,
starting with conics and ending with sheaves and cohomology. The
first chapter on conics is appropriate for first-year college
students (and many high school students). Chapter 2 leads the
reader to an understanding of the basics of cubic curves, while
Chapter 3 introduces higher degree curves. Both chapters are
appropriate for people who have taken multivariable calculus and
linear algebra. Chapters 4 and 5 introduce geometric objects of
higher dimension than curves. Abstract algebra now plays a critical
role, making a first course in abstract algebra necessary from this
point on. The last chapter is on sheaves and cohomology, providing
a hint of current work in algebraic geometry. This book is
published in cooperation with IAS/Park City Mathematics Institute.
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