Charles Babbage (1791–1871) is today remembered mainly for his attempt to complete his difference and analytical engines, the principles of which anticipate the major ideas of the modern digital computer. This book describes the evolution of Babbage's work on the design and implementation of the engines by means of a detailed study of his early mathematical investigations. Babbage is an almost legendary figure of the Victorian era, yet relatively little is known about him and no authoritative account of his life and work has appeared. He was primarily a mathematician and his early working life was devoted mainly to the study of pure mathematics. While containing much biographical information, this book concentrates on this crucial aspect of Babbage's work.