  The Tutorial reports recent experimental advances in studies of the dynamics
as well as the number and phase correlations of a Bose-Einstein condensed
photon gas confined in a high-finesse dye-filled microcavity. Repeated
absorption-emission-processes of photons on dye molecules here establish a
thermal coupling of the photonic quantum gas to both a heat bath and a particle
reservoir comprised of dye molecules. In this way, for the first time
Bose-Einstein condensation under grand-canonical statistical ensemble
conditions becomes experimentally accessible.
