This book is intended to be a textbook with systematic mathematical descriptions of five advanced topics in medical physics. These topics include Physics in Medical Linacs, Proton Therapy, Convolution and Superposition Dose Computation Algorithms, Dose Calculations with Boltzmann Transport Equation, Tumor Control and Normal Tissue Complication Probability Models. The book establishes fundamental understandings and introduces current advancements in these topics. It contains a great number of high quality images and mathematical equations to enhance the reading experience. There are also problems and questions at the end of each chapter. It should be of interests to the medical physics community. The advanced topics covered in this book are not covered well in traditional medical physics textbooks. This book is written as a synthesis from a large variety of sources so the readers can learn the topics from the book and have the capability to explore further readings. The topics in the book are developed with consistent mathematical notations from fundamental physics knowledge and equations. The topics covered in this book are self-contained study modules which can be used as textbook for graduate medical physics program, physics residency program, or self-study materials for practicing medical physicists. They are advanced topics for medical physicists to understand the current trend and developments in the field. The contents are well-written and illustrated for readers to develop quantitative understanding of the material. Due to its extensive content of the mathematical formulation in each topic, the prerequisite of the book is a bachelor's degree in physics and a graduate-level course in radiological physics. The book covers five topics in medical physics, which are independent of each other. The first chapter discusses the physics of electron acceleration in medical linacs. Maxwell's equation and boundary conditions are applied to develop quantitative understanding of various designs of waveguides. The content focuses on the derivations relevant to the electron acceleration mechanisms exploited by the medical linacs. The second chapter, proton therapy, introduces the history and treatment machine developments of several vendors. The focus is on the physics of the proton accelerators and transport subsystems. The pros and cons of the double scattering and the pencil beam scanning modalities are illustrated. It however does not provide in-depth details on proton treatment planning techniques. Chapter three discusses the popular photon convolution and superposition dose calculation algorithms, which are adopted by most of the commercial treatment planning systems. The major steps of these model-based algorithms are introduced in this chapter, including the calculations of incident energy fluence, kernels, medium heterogeneities and additional electron contaminations. The dose calculation algorithm by Boltzmann transport equation is gaining popularity in the medical physics community. Chapter four illustrates the deterministic transport approach to dose calculations for both photons and electrons. A particular helpful topic on Tumor Control and Normal Tissue Complication Probability Models is covered in chapter five. Not only the basic, but more advanced discussions on serial or parallel organ NTCP model and heterogeneity tumor control model formulations are addressed. The best aspect of this book is that it presents each topic from the perspective of fundamental physics principles and adheres to rigorous standards of mathematical presentation. It avoids superficial and qualitative presentation of core principles. Instead, the details are derived using consistent mathematical notation to facilitate the reading and understanding. This feature is unique from other available textbooks. The topics are all self-contained and up-to-date with the current state of technology development. The entire book provides a concise, easy to follow, bottom up approach to the topics. It is well-written and pleasant to read. The complete and systematic mathematical derivations in the book require the readers to possess a level of physics and mathematics background, including vector calculus, differential equations, advanced undergraduate electricity and magnetism, and matrix algebra to completely follow the materials. Nonetheless, it is a great textbook for individuals to acquire understanding of these advanced topics on a fundamental level. Wei Zou is an assistant professor at the University of Pennsylvania, Perelman School of Medicine, Department of Radiation Oncology. Her research interests are advanced techniques in radiation therapy and proton radiotherapy.