Many of the processes used in a metal casting are empirical in nature, but many others are deeply rooted in mathematics. In whatever form, casting of metals is an activity fundamental in the very existence of our world, as we know it today. Foundry reports indicate that solidification modelling is not only a cost-effective investment but also a major technical asset. It helps foundries move into markets with more complex and technically demanding work. However, to the best of the author's knowledge, there have been no attempts to synthesize the information that can be used for engineering calculations pertinent to computational modelling of casting solidification. This book attempts to describe solidification theory through the complex mathematical apparatus that includes partial differential equations and numerical analysis, which are required for a fundamental treatment of the problem. The mathematics, however, is restricted to the element essential to attain a working knowledge of the field. This is in line with the main goal of the book, which is to educate the reader in the fast moving area of computational modelling of solidification of casting.