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This book is intended for self-study or as a textbook for graduate students or advanced undergraduates. It presupposes some basic knowledge of pointset topology and a solid foundation in linear algebra. Otherwise, it develops all of the commutative algebra, sheaf-theory and cohomology needed to understand the material. This is the kind of background students might have at a school that emphasizes applied mathematics, or one where enrollment is not sufficient to run separate courses in commutative algebra. A classical result Affine varieties Local properties of affine varieties Varieties and Schemes Projective varieties Curves Appendixes Algebra Sheaves and ringed spaces Cohomology Solutions to Selected Exercises