We give in this lecture an introduction to the physics of two-dimensional (2d) Bose gases. We first discuss the properties of uniform, infinite 2d Bose fluids at non-zero temperature T. We explain why thermal fluctuations are strong enough to destroy the fully ordered state associated with Bose-Einstein condensation, but are not strong enough to suppress superfluidity in an interacting system at low T. We present the basics of the Berezinskii-Kosterlitz-Thouless theory, which provides the general framework for understanding 2d superfluidity. We then turn to experimentally relevant finite-size systems, in which the presence of residual “quasi–long-range” order at low temperatures leads to an interesting interplay between superfluidity and condensation. Finally we summarize the recent progress in theoretical understanding and experimental investigation of ultracold atomic gases confined to a quasi-2d geometry.