  We present a description of the adaptive mesh refinement (AMR) implementation
of the PLUTO code for solving the equations of classical and special
relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits,
in addition to the static grid version of the code, the distributed
infrastructure of the CHOMBO library for multidimensional parallel computations
over block-structured, adaptively refined grids. We employ a conservative
finite-volume approach where primary flow quantities are discretized at the
cell-center in a dimensionally unsplit fashion using the Corner Transport
Upwind (CTU) method. Time stepping relies on a characteristic tracing step
where piecewise parabolic method (PPM), weighted essentially non-oscillatory
(WENO) or slope-limited linear interpolation schemes can be handily adopted. A
characteristic decomposition-free version of the scheme is also illustrated.
The solenoidal condition of the magnetic field is enforced by augmenting the
equations with a generalized Lagrange multiplier (GLM) providing propagation
and damping of divergence errors through a mixed hyperbolic/parabolic explicit
cleaning step. Among the novel features, we describe an extension of the scheme
to include non-ideal dissipative processes such as viscosity, resistivity and
anisotropic thermal conduction without operator splitting. Finally, we
illustrate an efficient treatment of point-local, potentially stiff source
terms over hierarchical nested grids by taking advantage of the adaptivity in
time. Several multidimensional benchmarks and applications to problems of
astrophysical relevance assess the potentiality of the AMR version of PLUTO in
resolving flow features separated by large spatial and temporal disparities.
