Dynamics of a Trapped Bose-Condensed Gas at Finite Temperatures

The experimental achievement in 1995 of Bose-Einstein condensation (BEC) intrapped laser-cooled atomic gases has opened up an exciting field ofresearch on a new superfluid phase of mater. In this talk, I will reviewrecent theoretical studies on the dynamics of trapped Bose-condensed gasesat finite temperatures. In the second part of the talk, I will also discussa kinetic theory for a spin-1/2 Bose gas, in connection with recent JILAexperiments on the collective spin dynamics in a trapped gas of Rb-87 atomswith two hyperfine states.