An Introduction to Computational Materials Science - Principles and Applications focuses on the fundamental methods and universal principles of computational materials science, providing a comprehensive knowledge of computational simulations of materials behaviour. Examines materials modelling at a wide range of scales, from electronic structure methods to microstructure evolution, covering key methods from the atomic to the mesoscopic scale, including density general function theory, molecular dynamics, Monte Carlo methods, metacellular automata and phase field methods. The fundamental equations used in materials modelling are explained in detail and summarised with mathematical background. An extensive appendix is also given, including basic background on materials science, classical mechanics, quantum mechanics, statistical thermodynamics and linear elasticity.