The main aim of this book is to, present a completely algebraic approach to the Enriques' classification of smooth projective surfaces defined over an algebraically dosed field of arbitrary characteristic. This algebraic approach is one of the novelties in comparison to existing textbooks on the subject. In the new edition of this book, two chapters as well as exercises at the end of each chapter have been added. One new chapter deals with various applications of the Zariski decomposition of an effective divisor, and the other discusses some results on surfaces that were found after the publication of the first edition. For a reader who has completed a first course in algebraic geometry, the present book is completely self-contained. It can be used as a textbook for a graduate course on surfaces or as a resource for researchers and graduate students in algebraic geometry and related fields.