"Although the theory of s (s where the underlying space is a and the group operations are ) goes back to around 1870 the theory of topological groups in a more general sense seem not to have been considered until 1925 when and , independently, made the basic definitions, rather in the spirit of , and since then this too has developed into a major branch of . It was Weil (1937) who wrote the first definitive study of s and applied the theory to both s and topological groups. However the basic idea was already emerging early in the century, indeed the concepts of and were well understood by Weierstrass and by Cauchy before him."