Originally published in 1946, this book was prepared by the Committee for the Calculation of Mathematical Tables. The text contains a series of tables of Legendre polynomials, created to meet the needs of researchers in various branches of mathematics and physics. The tables were largely designed by Leslie John Comrie (1893–1950), an astronomer who was integral to the development of mechanical computation. This book will be of value to anyone with an interest in Legendre polynomials and mathematical tables.