Shock breakout theory
  The earliest supernova (SN) emission is produced when the optical depth of
the plasma lying ahead of the shock, which ejects the envelope, drops below
c/v, where v is the shock velocity. This "breakout" may occur when the shock
reaches the edge of the star, producing a bright X-ray/UV flash on time scales
of seconds to a fraction of an hour, followed by UV/optical "cooling" emission
from the expanding cooling envelope on a day time-scale. If the optical depth
of circumstellar material (CSM) ejected from the progenitor star prior to the
explosion is larger than c/v, the breakout will take place at larger radii,
within the CSM, extending its duration to days time scale. The properties of
the early, breakout and cooling, emission carry unique signatures of the
structure of the progenitor star (e.g. its radius and surface composition) and
of its mass-loss history. The recent progress of wide-field transient surveys
enable SN detections on a day time scale, and are being used to set unique
constraints on the progenitors of SNe of all types. This chapter includes a
pedagogical description of SN breakout theory, and a concise overview of what
we have learned from observations so far, and of advances in observational
capabilities that are required in order to make further significant progress.
