This book is devoted to an exposition of the theory of finite-dimensional Lie groups and Lie algebras, which is a beautiful and central topic in modern mathematics. At the end of the nineteenth century this theory came to life in the works of Sophus Lie. It had its origins in Lie's idea of applying Galois theory to differential equations and in Klein's "Erlanger Programm" of treat- ing symmetry groups as the fundamental objects in geometry. Lie's approach to many problems of analysis and geometry was mainly local, that is, valid in local coordinate systems only. At the beginning of the...

I am sure that something must be found. There must exist a notion of generalized functions which are to functions what the real numbers are to the rationals (G. Peano, 1912) Not that much effort is needed, for it is such a smooth and simple theory (F. Treves, 1975) In undergraduate physics a lecturer will be tempted to say on certain occasions: "Let ?. x/ be a function on the line that equals 0 away from 0 and is in?nite at 0 in such a way that its total integral is 1. The most important property of ?. x/ is exempli?ed Z by the identity 1 . x/?. x/ dx D . 0/; 1 where is any continuous...