  The univariate extreme value theory deals with the convergence in type of
powers of elements of sequences of cumulative distribution functions on the
real line when the power index gets infinite. In terms of convergence of random
variables, this amounts to the the weak convergence, in the sense of
probability measures weak convergence, of the partial maximas of a sequence of
independent and identically distributed random variables. In this monograph,
this theory is comprehensively studied in the broad frame of weak convergence
of random vectors as exposed in Lo et al.(2016). It has two main parts. The
first is devoted to its nice mathematical foundation. Most of the materials of
this part is taken from the most essential Lo\`eve(1936,177) and Haan (1970),
based on the stunning theory of regular, pi or gamma variation. To prepare the
statistical applications, a number contributions I made in my PhD and my
Doctorate of Sciences are added in the last chapter of the last chapter of that
part. Our real concern is to put these materials together with others, among
them those of the authors from his PhD dissertations and Science doctorate
thesis, in a way to have an almost full coverage of the theory on the real line
that may serve as a master course of one semester in our universities. As well,
it will help the second part of the monograph. This second part will deal with
statistical estimations problems related to extreme values. It addresses
various estimation questions and should be considered as the beginning of a
survey study to be updated progressively. Research questions are tackled
therein. Many results of the author, either unpublished or not sufficiently
known, are stated and/or updated therein.
