  Recent developments in the physics of ultracold gases provide wide
possibilities for reducing the dimensionality of space for magnetically or
optically trapped atoms. The goal of these lectures is to show that regimes of
quantum degeneracy in two-dimensional (2D) and one-dimensional (1D) trapped
gases are drastically different from those in three dimensions and to stimulate
an interest in low-dimensional systems. Attention is focused on the new physics
appearing in currently studied low-dimensional trapped gases and related to
finite-size and finite-temperature effects.
