This book is the fruit of many years of experience on the creation of synthetic worldsandvirtualrealities.Ourgoalistotransmitthisexperiencetostudents and ease the learning curve required to master the creation of Virtual Reality (VR) applications. We start by providing some brief answers to key questions such as: where did VR come from? what are the main concepts that help us understand this research ?eld? what are the current VR trends? and last but not least, how can we create virtual worlds? Throughout the book we consider the terms “virtual environment,” “v- tualworld”and“VRapplication”asequivalentconcepts:computer-generated environments mainly composed of interactive computer graphics, designed to physically and/or psychologically immerse one or more users in an alternative reality. The ?rst part of the book makes a review of the basic theoretical and practical concepts involved in the visual aspect of virtual environments. We startbypresentingthebasicmathematicalfoundationsforthesynthesisof3D graphics,includingbasicmodelingandrenderingtechniques.Acomprehensive review of the state of the art of computer animation closes this part.