This book offers a focused collection of lectures and tutorials on applying machine learning techniques to research in theoretical physics and pure mathematics. Machine learning continues to transform the scientific landscape, providing powerful tools capable of driving significant advances across these disciplines. Through clear conceptual explanations and practical examples, this text equips students and researchers with the knowledge and skills needed to integrate these methods into their own work.The book begins with an introduction to the core principles of machine learning, including neural networks and transformer architectures. It then explores advanced optimization and search strategies, with an in-depth look at genetic algorithms, quantum annealing, and reinforcement learning. In the final chapters, these techniques are applied to contemporary problems in string theory and knot theory, illustrating their potential in cutting-edge research contexts. Throughout, the material is reinforced with worked examples and accompanied by code implementations to support hands-on learning.Designed for graduate students and researchers in physics and mathematics, this book serves as an accessible yet rigorous introduction to the practical use of machine learning in modern scientific research.