We study the properties of magnetically trapped atomic Bose gases with
both negative and positive scattering lengths. We present theoretical
results for the temperature dependence of the condensate fraction and
for other quantities characterizing the thermodynamics of the trapped
gas. We investigate the structure of the elementary excitations, incl
uding quantized vortices. We explore the behavior of the condensate wa
ve function near the boundary with possible application to Josephson-t
ype effects.