Artificial Intelligence (AI) has emerged as one of the most transformative technologies of the twenty-first century, revolutionizing industries, reshaping societies, and redefining the way humans interact with machines. From intelligent virtual assistants and autonomous systems to predictive analytics and generative AI models, the rapid advancement of AI has been driven by strong mathematical principles. Behind every machine learning algorithm, neural network, optimization technique, and intelligent decision-making system lies a rich foundation of mathematics. Understanding these foundations is essential for students, researchers, educators, and practitioners seeking to develop a deep and meaningful understanding of Artificial Intelligence. The book "Mathematical Foundations of Artificial Intelligence" has been carefully designed to provide a comprehensive and systematic introduction to the mathematical concepts that underpin modern AI technologies. This multi-author volume brings together the expertise of academicians and researchers who have extensive experience in mathematics, computational sciences, engineering education, and interdisciplinary research. Their collective efforts have resulted in a text that bridges theoretical rigor with practical relevance, making advanced mathematical concepts accessible to a broad audience. The primary objective of this book is to establish a strong mathematical framework for understanding AI algorithms and intelligent systems. The contents cover essential topics including set theory, relations, functions, linear algebra, matrix operations, eigenvalues and eigenvectors, calculus, optimization techniques, probability theory, statistics, mathematical logic, graph theory, combinatorics, information theory, and reinforcement learning mathematics. In addition, the book explores modern developments such as probabilistic graphical models, neural network mathematics, explainable AI, and the mathematical foundations of large language models. Special emphasis has been placed on demonstrating how mathematical concepts translate into real-world AI applications. Each chapter provides a logical progression from fundamental principles to advanced topics, supported by illustrative examples, conceptual explanations, and application-oriented discussions. This approach enables readers not only to understand the mathematics behind AI but also to appreciate its practical significance in solving complex computational problems. The authors believe that a solid understanding of mathematics is indispensable for innovation in Artificial Intelligence. As AI continues to evolve and influence diverse domains such as healthcare, finance, education, cybersecurity, robotics, and data science, the demand for mathematically proficient professionals will continue to grow. This book aims to equip learners with the analytical tools necessary to contribute effectively to this rapidly expanding field. This volume is intended for undergraduate and postgraduate students of Mathematics, Computer Science, Artificial Intelligence, Data Science, Machine Learning, and related disciplines. It will also serve as a valuable reference for researchers, faculty members, industry professionals, and anyone interested in exploring the mathematical foundations that drive intelligent technologies. The editors and authors express their sincere gratitude to colleagues, students, researchers, and academic institutions whose support and encouragement have contributed to the successful completion of this work. We hope that this book will inspire readers to appreciate the elegance of mathematics and its central role in advancing Artificial Intelligence. We trust that "Mathematical Foundations of Artificial Intelligence" will serve as a valuable academic resource and a guiding reference for learners and professionals seeking to build a strong foundation in the mathematics that powers the intelligent systems of today and tomorrow.