This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, like 'Algebraic Varieties', whose natural continuation is a more advanced course on the theory of schemes, vector bundles and sheaf-cohomology.Valuable to students studying Algebraic Geometry and Geometry, A First Course in Algebraic Geometry and Algebraic Varieties contains around 60 solved exercises to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full details.Many examples are discussed which reinforces the understanding of both the theoretical elements and their consequences as well as the possible applications of the material.