  We propose an elementary introduction to the finite volume method in the
context of gas dynamics conservation laws. Our approach is founded on the
advection equation, the exact integration of the associated Cauchy problem, and
the so-called upwind scheme in one space dimension. It is then extended in
three directions: hyperbolic linear systems and particularily the system of
acoustics, gas dynamics with the help of the Roe matrix and two space
dimensions by following the approach proposed by Van Leer. A special emphasis
on boundary conditions is proposed all along the text.
