  In the footsteps of the book \textit{Measure Theory and Integration By and
For the Learner} of our series in Probability Theory and Statistics, we
intended to devote a special volume of the very probabilistic aspects of the
first cited theory. The book might have assigned the title : From Measure
Theory and Integration to Probability Theory. The fundamental aspects of
Probability Theory, as described by the keywords and phrases below, are
presented, not from experiences as in the book \textit{A Course on Elementary
Probability Theory}, but from a pure mathematical view based on Measure Theory.
Such an approach places Probability Theory in its natural frame of Functional
Analysis and constitutes a firm preparation to the study of Random Analysis and
Stochastic processes. At the same time, it offers a solid basis towards
Mathematical Statistics Theory. The book will be continuously updated and
improved on a yearly basis.
