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The book presents a comprehensive overview of modern mathematical concepts, models, methods and tools with applications in computer graphics, computer vision and machine learning. Fifteen topics in modern mathematics are arranged in three parts: algebra, geometry and topology, with an emphasis on tensors and manifolds. and a separate part on applications. It can be used as a textbook for a selected topics course at the undergraduate or graduate level. It can also be used as fifteen short crash courses for self-study of any of the topics in any order, with minimal inter-chapter dependencies. This book is based on the lecture notes of two courses the author has taught in the US "Gaming Mathematics" at the undergraduate level and "Mathematical Methods in Computer Graphics and Vision" at the graduate level, with considerable expansions.