"Mathematical Theories of Machine Learning - Theory and Application" is a book that examines the deep mathematical foundations and theories that underlie modern machine learning systems. The authors cover various mathematical concepts in detail, such as linear algebra, probability theory, statistics, optimization, and numerical methods, and show how they are applied in machine learning models. This book not only provides theoretical information, but also offers concrete examples of the application of mathematical approaches to solving real machine learning problems. The main algorithms and methods of training models are highlighted, their properties and effectiveness are investigated, which helps readers gain an understanding of the processes that take place inside training models. "Mathematical Theories of Machine Learning - Theory and Application" is intended for specialists in the field of machine learning, researchers, students and anyone interested in the mathematical basis of modern methods of machine learning."