  The properties of phase transitions and the types of order present in the
low-temperature states of matter are fundamentally dependent on the
dimensionality of physical systems. Generally, highly ordered states are more
robust in higher dimensions, while thermal and quantum fluctuations, which
favour disordered states, play a more important role in lower dimensions. The
case of a two-dimensional (2d) Bose fluid is particularly fascinating because
of its "marginal" behaviour. In an infinite uniform 2d fluid thermal
fluctuations at any non-zero temperature 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, but non-zero
temperatures. Further, the presence of residual "quasi-long-range" order at low
temperatures leads to an interesting interplay between superfluidity and
condensation in all experimentally relevant finite-size systems. In these notes
we give an introduction to the physics of 2d Bose fluids from an atomic physics
perspective. Our goal is to summarize the recent progress in theoretical
understanding and experimental investigation of ultra-cold atomic gases
confined to 2d geometry, and we also hope to provide a useful introduction to
these systems for researchers working on related topics in other fields of
physics.
