Abstract : The aim of this paper is to summarize the probability theory of quantile functions. The contributions of this paper are: (1) to emphasize the duality of quantile functions with distribution functions (sec. 1); (2) to explicitly define the notions of 'convergence in quantile' and 'convergence in r-mean quantile' (sec 2); (3) provide simple proofs of the distribution theory of extreme values (sec 4); and (4) emphasize the role of tail exponents of quantile functions and density-quantile functions in providing easy to apply criteria for the extreme value distributions corresponding to a specified distribution. (Author)