This textbook establishes a theoretical framework for understanding deep learning models of practical relevance. With an approach that borrows from theoretical physics, Roberts and Yaida provide clear and pedagogical explanations of how realistic deep neural networks actually work. To make results from the theoretical forefront accessible, the authors eschew the subject's traditional emphasis on intimidating formality without sacrificing accuracy. Straightforward and approachable, this volume balances detailed first-principle derivations of novel results with insight and intuition for theorists and practitioners alike. This self-contained textbook is ideal for students and researchers interested in artificial intelligence with minimal prerequisites of linear algebra, calculus, and informal probability theory, and it can easily fill a semester-long course on deep learning theory. For the first time, the exciting practical advances in modern artificial intelligence capabilities can be matched with a set of effective principles, providing a timeless blueprint for theoretical research in deep learning. Detailed step-by-step explanations for all equations and clear exposition of both old and new concepts in deep learning theory make the book accessible to readers with a minimal prerequisite of linear algebra, calculus, and informal probability theory Many novel results that appear for the first time in the literature, taking readers to the forefront of deep learning theory Provides a unique approach that bridges deep learning and theoretical physics, demonstrating to the ML community how a theoretical physics approach can be useful, while also teaching techniques that are valuable for theoretical physicists