Rodrigues' Formula is a specialized book that deals with a significant mathematical concept known as Rodrigues' formula. This formula, which was independently developed by Olinde Rodrigues, Sir James Ivory, and Jacobi, plays a central role in the theory of Legendre polynomials. The term 'Rodrigues' formula' was introduced by Heine in 1878 to honor Rodrigues' discovery. The book provides a detailed analysis and historical perspective on the development of this formula and its applications in mathematics. It is aimed at students and professionals seeking a deeper understanding of the mathematical foundations and the associated theories. The comprehensive presentation of the topic makes it a valuable resource for anyone engaged in mathematics and the natural sciences.