  We consider the magnetic and spin evolution of isolated neutron stars
assuming that the magnetic field is initially confined to the crust. The
evolution of the crustal field is determined by the conductive properties of
the crust which, in its turn, depend on the thermal history of the neutron
star. Due to this fact, a study of the magnetic field decay may be a powerful
diagnostic of the properties of matter in the core where the density is above
the nuclear density. We treat the evolution of neutron stars for different
possible equations of state and cooling scenarios (standard and, so called,
accelerated cooling).
  The spin evolution is strongly influenced by the behaviour of the magnetic
field. Assuming that the spin-down rate of the neutron star is determined by
the magnetodipole radiation, we calculated the evolutionary tracks of isolated
pulsars in the $B - \tau$ and $B-P$ planes, where $B$ and $P$ are the magnetic
field and period, respectively, and $\tau$ is the spin-down age. The calculated
tracks are compared with observational data on the magnetic field and period of
pulsars. This comparison allows to infer the most suitable equations of state
of nuclear matter and cooling model and to determine the range of parameters of
the original magnetic configurations of pulsars.
