Topics in the theory of the ultracold dilute alkali gases

These lectures address Bose and Fermi ultracold dilute alkali gases. For Bose gases I discuss general BEC concepts, superfluidity, the Josephson effect, and issues related to the establishment of a 'phase standard'. For Fermi gases I discuss prospects for Cooper pairing and its detection. The four lectures on alkali Bose gases which I actually gave at the School were based on a review paper in preparation for Reviews of Modern Physics. In order to avoid extensive duplication of the contents of that review, what I present here, condensed into three lectures, is a melange of informal commentary on the results presented there and some material which for space and other reasons had to be omitted. This material is ideally read in conjunction with the review. The fourth lecture, on the Fermi alkali gases, is presented here in (nearly) the form in which it was actually given.