Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical
normal random variables. Their theory presents a powerful range of tools for probabilistic
modelling in various academic and technical domains such as Statistics Forecasting Finance
Information Transmission Machine Learning - to mention just a few. The objective of these
Briefs is to present a quick and condensed treatment of the core theory that a reader must
understand in order to make his own independent contributions. The primary intended readership
are PhD Masters students and researchers working in pure or applied mathematics. The first
chapters introduce essentials of the classical theory of Gaussian processes and measures with
the core notions of reproducing kernel integral representation isoperimetric property large
deviation principle. The brevity being a priority for teaching and learning purposes certain
technical details and proofs are omitted. The later chapters touch important recent issues not
sufficiently reflected in the literature such as small deviations expansions and
quantization of processes. In university teaching one can build a one-semester advanced course
upon these Briefs.?rious academic and technical domains such as Statistics Forecasting
Finance Information Transmission Machine Learning - to mention just a few. The objective of
these Briefs is to present a quick and condensed treatment of the core theory that a reader
must understand in order to make his own independent contributions. The primary intended
readership are PhD Masters students and researchers working in pure or applied mathematics. The
first chapters introduce essentials of the classical theory of Gaussian processes and measures
with the core notions of reproducing kernel integral representation isoperimetric property
large deviation principle. The brevity being a priority for teaching and learning purposes
certain technical details and proofs are omitted. The later chapters touch important recent
issues n
