This book provides an introduction to abstract algebraic geometry. The prerequisites for this approach are results from commutative algebra, which are stated as needed, and some elementary topology. There are more than 400 exercises throughout the book, offering specific examples as well as more specialized topics not treated in the main text. Three appendices present brief accounts of some areas of current research. This book can be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.