The recent observation of Bose-Einstein condensation (BEC) in dilute atomic gases is quite possibly the most exciting development in atomic, molecular, and optical physics since the invention of the laser. It provides us with an unprecedented opportunity to study coherent matter, because the relatively weak particle interactions render the theory tractable, while powerful experimental techniques provide detailed measurements of the condensate properties. This field is now in its infancy, and there are many open questions about condensate thermodynamic properties, collective and vortex excitations, the damping and (possibly nonlinear) couplings of these excitations, critical properties, optical properties, role of atomic interactions, stability with respect to recombination, behavior of negative scattering length condensates, finite size effects, and the role of internal degrees of freedom. Other fascinating questions concern the basic phenomenon itself: the formation of a coherent state of matter. The conditions under which the phase of this matter can be observed, and the extent to which it may vary in space or time, are of great interest. Perhaps the most exciting prospect is that processes related to Bose condensation might allow us to produce coherent matter wave sources, or "atom lasers." That is, we may be able to build a device that would put out a bright, monochromatic, diffraction-limited matter wave, with a coherence length much larger than the size of the source. An atom laser might find powerful applications in areas such as atom interferometry, atomic holography (i.e. the direct formation of a desired material object by coherent manipulation of the matter waves), or in other as yet unimagined areas. Various proposals for atom lasers include coherent coupling of atoms out of a condensate with simultaneous "pumping" of the condensate, and optical cycling of cold atoms into "lasing" atomic modes. In May, 1997, our group succeeded in producing a Bose-Einstein condensate! To our knowledge, we were the first to do so since the original groups at Colorado (JILA), M.I.T., and Rice. Our apparatus is illustrated above. We also show a plot of the path to BEC in phase space taken by our experiment. We begin with a laser-slowed 87Rb atomic beam (increasing-field Zeeman slower). Atoms emerge from the slower at a velocity of about 30 m/s, and are captured into a "magneto-optic trap" (MOT). We load about 2 x 109 atoms into a bright MOT, then switch for 300 ms to a spatial forced dark MOT. In the next step, we turn off the MOT, and further reduce the temperature of the atoms to about 40 microKelvin with dark optical molasses laser cooling. After the sample as been optically trapped and cooled, we switch off all lasers and switch on a magnetic "TOP" trap, of the type first used by Eric Cornell and collaborators at JILA. At this stage, we end up with about 4 x 108 trapped atoms at a temperature of about 90 microKelvin. The cloud of atoms is then further cooled and compressed by increasing the strength of the TOP trap. During this stage, the density increases due to the compression, and there is also some evaporative cooling because the atoms may leave the trap through Majorana spin flips at the orbiting field zero ("death circle"). The radius of the death circle shrinks as the trap is compressed, ejecting successively colder and colder atoms as the compression proceeds. The radial oscillation frequency of the atoms in the TOP trap at maximum compression is about 90 Hz. Finally we complete the cooling with radio frequency induced evaporative cooling. During this stage, the spins of the hottest atoms are selectively flipped by resonant radio frequency transitions. The remaining atoms rethermalize at successively lower temperatures due to elastic collisions. Finally, we turn the cooling off, adiabatically ramp the TOP trap strength down until the radial oscillation frequency is 18 Hz, and suddenly switch off the trap. The atoms freely expand for 18 ms, and we take a time of flight (TOF) image of the expanding cloud. This image measures the velocity distribution of the expanding atoms (time-of-flight method). Several clear signatures of BEC are observed. The velocity distribution is smooth and symmetric above the calculated Tc, but acquires an asymmetric peak at temperatures slightly below Tc. The phase-space density of the expanding cloud also increases very rapidly with small changes in final rf frequency when the temperature is near Tc. We currently produce nearly pure condensates containing about 200,000 atoms. Now, we are pursuing some of the many directions made possible by this exciting development. We are particularly interested in studying the coherence properties of the condensate, the properties of a condensate with non-zero angular momentum, and the role of atomic interactions in Bose-condensation. Further down the road, we plan to carry out experiments in atom optics using a Bose condensate as a source. Finally, we are pursuing some of our own ideas on how to build an atom laser.