This book explores the visualization of three-dimensional non-Euclidean spaces using ray-tracing techniques in Graphics Processing Unit (GPU). This is a trending topic in mathematical visualization that combines the mathematics areas of geometry and topology, with visualization concepts of computer graphics. Several conditions made this a special moment for such topic. On one hand, the development of mathematical research, computer graphics, and algorithms have provided the necessary theoretical framework. On the other hand, the evolution of the technologies and media allows us to be immersed in three-dimensional spaces using Virtual Reality. The content of this book serves both experts in the areas and students. Although this is a short book, it is self-contained since it considers all the ideas, motivations, references, and intuitive explanations of the required fundamental concepts.

List of Figures.- Introduction.- Mathematical Background.- Visualization of Three-Dimensional Spaces.- Immersive Visualization.- Riemannian Ray Tracing.- Classical lowercase {non.- Nil, SL2, and Sol.- Curved 3D Spaces.- Photo-Realism.- Bibliography.- Authors' Biographies.