  We update the capabilities of the software instrument Modules for Experiments
in Stellar Astrophysics (MESA) and enhance its ease of use and availability.
Our new approach to locating convective boundaries is consistent with the
physics of convection, and yields reliable values of the convective core mass
during both hydrogen and helium burning phases. Stars with $M<8\,{\rm M_\odot}$
become white dwarfs and cool to the point where the electrons are degenerate
and the ions are strongly coupled, a realm now available to study with MESA due
to improved treatments of element diffusion, latent heat release, and blending
of equations of state. Studies of the final fates of massive stars are extended
in MESA by our addition of an approximate Riemann solver that captures shocks
and conserves energy to high accuracy during dynamic epochs. We also introduce
a 1D capability for modeling the effects of Rayleigh-Taylor instabilities that,
in combination with the coupling to a public version of the STELLA radiation
transfer instrument, creates new avenues for exploring Type II supernovae
properties. These capabilities are exhibited with exploratory models of
pair-instability supernova, pulsational pair-instability supernova, and the
formation of stellar mass black holes. The applicability of MESA is now widened
by the capability of importing multi-dimensional hydrodynamic models into MESA.
We close by introducing software modules for handling floating point exceptions
and stellar model optimization, and four new software tools -- MESAWeb,
MESA-Docker, pyMESA, and mesastar.org -- to enhance MESA's education and
research impact.
