  The motion of a fully ionized plasma of electrons and ions is generally
governed by the Vlasov-Maxwell-Landau system. We prove the global existence of
solutions near Maxwellians to the Cauchy problem of the system for the
long-range collision kernel of soft potentials, particularly including the
classical Coulomb collision, provided that initial data is smooth enough and
decays in velocity variable fast enough. As a byproduct, the convergence rates
of solutions are also obtained. The proof is based on the energy method through
designing a new temporal energy norm to capture different features of this
complex system such as dispersion of the macro component in $\mathbb{R}^3$,
singularity of the long-range collisions and regularity-loss of the
electromagnetic field.
