In this thesis, we present a detailed theoretical study of a coupled two-component Bose- Einstein condensate in a magnetic trap. We first present a quantum kinetic theory describ- ing the Bose-condensed gas, that applies to general finite-temperature and nonequilibrium situations. We then treat the coupled, two-component condensate at zero-temperature by solving the Gross-Pitaevskii equation, in which the fluctuations are neglected. We show that in the weak-coupling limit, the system behaves like a nonlinear Josephson-junction, analogous to two condensates in a double-well potential that are coupled due to quantum tunneling. In the opposite limit of strong coupling between internal states, we show that the condensate can be prepared in a variety of new topological states. In particular, we predict a scheme for generating a quantized vortex in this two-component system, where one component sits in the center with a uniform phase while the other circulates around it. Subsequent related experimental work at JILA by the group of Eric Cornell and Carl Wie- man has demonstrated these predictions in the laboratory \textemdashthis is the first observation of a vortex in a dilute-gas Bose-Einstein condensate. Finally, we study the kinetic evolution of a single-component gas above the critical temperature by solving the Boltzmann equation and investigate the possibility of achieving a steady-state condensation, which can occur if atoms are injected into the trap during evaporative cooling.

}, year = {1999}, publisher = {University of Colorado Boulder}, }