  A survey is given of the present state of the art in studying Bose-Einstein
condensation of dilute atomic gases. The bulk of attention is focused on the
principal theoretical problems, though the related experiments are also
mentioned. Both uniform and nonuniform trapped gases are considered. Existing
theoretical contradictions are critically analysed. A correct understanding of
the principal theoretical problems is necessary for gaining a more penetrating
insight into experiments with trapped atoms and for their proper
interpretation.
