This book gives an overview of the most important foundations of statistical computing with particular emphasis on the historical development. The book will not provide a description of all numerical algorithms in current use for statistical computations. Instead, the book focuses on the most important construction principles for these algorithms. Our aim is to enable the reader, after working through the material covered in the book, to quickly understand the main ideas of modern numerical algorithms because he or she has seen and understood the underlying principles of these algorithms. We feel this capacity is much more valuable to both practitioners and theorists than having memorized the current, and soon to be outdated, set of popular algorithms from computational statistics.