Andrew Russell Forsyth (1858–1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1927, this book constitutes Forsyth's attempt at a systematic exposition of the calculus of variations. It was created as the antidote to a perceived lack of continuity in the development of the topic. Ambitious and highly detailed, this book will be of value to anyone with an interest in the calculus of variations and the history of mathematics in general.