This book provides an overview of the mathematical methods used in Physics at the graduate level, covering the mathematical topics that will be needed in other core graduate-level Physics courses such as Classical Mechanics, Quantum Mechanics, and Electrodynamics. It is based on lecture notes for a one-semester introductory graduate level course and covers the material through detailed step-by-step worked examples. The goal of this work is to equip the student with a grounding in topics such as complex analyses, linear algebra, vector calculus, methods of integration, ordinary and partial differential equations, and variational calculus that are needed for graduate-level coursework in Physics. The book is sectioned into modules, each one starting from a familiar material and progressing to more advanced concepts. Each module builds upon previous ones, ultimately developing an essential repository of mathematical tools.
