  We discuss the relationships between some classical representations of the
fractional Brownian motion, as a stochastic integral with respect to a standard
Brownian motion, or as a series of functions with independent Gaussian
coefficients. The basic notions of fractional calculus which are needed for the
study are introduced. As an application, we also prove some properties of the
Cameron-Martin space of the fractional Brownian motion, and compare its law
with the law of some of its variants. Several of the results which are given
here are not new; our aim is to provide a unified treatment of some previous
literature, and to give alternative proofs and additional results; we also try
to be as self-contained as possible.
