  We give a general introduction to quantum phase transitions in
strongly-correlated electron systems. These transitions which occur at zero
temperature when a non-thermal parameter $g$ like pressure, chemical
composition or magnetic field is tuned to a critical value are characterized by
a dynamic exponent $z$ related to the energy and length scales $\Delta$ and
$\xi$. Simple arguments based on an expansion to first order in the effective
interaction allow to define an upper-critical dimension $D_{C}=4$ (where
$D=d+z$ and $d$ is the spatial dimension) below which mean-field description is
no longer valid. We emphasize the role of pertubative renormalization group
(RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF)
theories to understand the quantum-classical crossover in the vicinity of the
quantum critical point with generalization to the Kondo effect in heavy-fermion
systems. Finally we quote some recent inelastic neutron scattering experiments
performed on heavy-fermions which lead to unusual scaling law in $\omega /T$
for the dynamical spin susceptibility revealing critical local modes beyond the
itinerant magnetism scheme and mention new attempts to describe this local
quantum critical point.
