Unlike other books on algebraic geometry, this text includes applications from various areas of mathematics, biology, and physics. Designed for advanced undergraduate and graduate students with an applied mathematics background, the book develops most of the necessary commutative algebra. It describes all of the algebraic and geometric concepts required for understanding algebraic geometry. The author also presents a very recent and simpler proof of the dimension of an affine variety. A solutions manual and figure slides are available with qualifying course adoption.