This book provides an in-depth look at the mathematical foundations and technologies behind many machine learning algorithms. It begins with an introductory chapter that outlines the notation used throughout the text. This chapter serves as a refresher on essential concepts from calculus, linear algebra, and probability, and introduces basic terms from measure theory, which are useful for navigating the more technical sections of the book. Additionally, the introduction covers background material in matrix analysis and optimization, setting the stage for the algorithms discussed later. The subsequent chapters delve into the theoretical underpinnings of various algorithms, such as stochastic gradient descent and proximal methods. After establishing the basics of statistical prediction, the book explores reproducing kernel theory and Hilbert space techniques, which are crucial across multiple applications. The text then presents detailed descriptions of several supervised statistical learning algorithms, including linear methods, support vector machines, decision trees, boosting techniques, and neural networks. The focus then shifts to generative methods. The book introduces sampling techniques and Markov chain theory, which are fundamental for understanding generative models. Following this, it covers the theory of graphical models and an introduction to variational methods for models with latent variables. These concepts are further expanded upon in the sections dedicated to generative models based on deep learning. Next, the book delves into unsupervised learning methods, discussing clustering, factor analysis, and manifold learning. These techniques are essential for tasks where labeled data is not available, allowing the identification of patterns and structures within datasets. Finally, the book concludes with a theoretical chapter on concentration inequalities and generalization bounds. This section provides a rigorous mathematical framework for understanding how well machine learning models generalize from training data to unseen data, which is critical for ensuring the reliability and effectiveness of these models. Overall, this comprehensive resource is designed to equip readers with a solid understanding of both the practical and theoretical aspects of machine learning, making it invaluable for students, researchers, and practitioners in the field.