My talk will emphasize the fact that a phase transition in a finite system is smooth --- rather than critical, as it is for the case of a bulk system. This point will be illustrated using a simple calculation that explores the onset of Bose-Einstein condensation in one dimension. If time permits, I will discuss this problem in three dimensions as well, both for free particles and for particles confined to harmonic traps.

My talk will be based on several papers that I have published in the Physical Review and in the American Journal of Physics.