  The main aim of this article is to develop, in a fully detailed fashion, a
{\bf unified} theory of the spectral theory of mean values of individual
automorphic L-functions which is a natural extension of the fourth moment of
the Riemann zeta-function but does not admit any analogous argument and
requires a genuinely new method. Thus we first develop a relatively
self-contained account of the theory of automorphic representations, especially
highlighting the Kirillov model, with which we resolve the problem on the mean
value of those L-functions. As another reward, we gain a geometrical
understanding of sum formulas involving Kloosterman sums, which is in fact a
considerably simplified account of Cogdell-Piatetski-Shapiro's method. Our
reasoning is quite explicit in contrast to theirs.
