  This is an introduction to the theoretical physics of metals for students and
physicists from other specialities. Certain simple consequences of the Fermi
statistics in pure metals are first addressed, namely the Peierls distortion,
Kohn anomalies and the Labb\'e-Friedel distortion. Then the physics of dilute
alloys is discussed. The analogy with nuclear collisions was a fruitful
starting point, which suggested one should analyse the effects of impurities in
terms of a scattering problem with the introduction of phase shifts. Starting
from these concepts, Friedel derived a theory of the resistivity of alloys, and
a celebrated sum rule relating the phase shifts at the Fermi level to the
number of electrons in the impurity, which turned out to play a prominent role
later in the context of correlated impurities, as for instance in the Kondo
effect. Friedel oscillations are also an important result, related to
incommensurate magnetic structures. It is shown how they can be derived in
various ways: from collision theory, perturbation theory, self-consistent
approximations and Green's function methods. While collision theory does not
permit to take the crystal structure into account, which is responsible for
electronic bands, those effects can be included in other descriptions, using
for instance the tight binding approximation.
