This book provides an introduction to earthquake source physics, at the heart of modern earthquake seismology. It employs a unique dual approach for grasping the physics both from mathematical and numerical analyses; examples of Fortran programs are also included. The book consists of two parts. Part I is designed as a first course to give undergraduate students a theoretical understanding of the framework of earthquake modelling. It clearly explains the fundamental concepts with mathematical methods: the linear elastic theory for the representation theorem, the fracture mechanics that describes two-dimensional static and dynamic crack growth. Numerical analysis accompanies a consistent framework of the Boundary Integral Equation Method, which provides a systematic set of computer programs to assist students as they simulate earthquake rupture processes. Each chapter includes detailed exercises that allow students to apply the methods they have learned to calculate pertinent results. PartII is designed for graduate students and consists of advanced topics: introduction of the latest friction theory, poroelasticity, earthquake sequences, and plasticity. This work is aimed at a wide range of readers and is especially relevant for graduate students and solid-earth researchers who wish to become more familiar with the field.