Bose-Einstein condensation (BEC) in ultra-cold magnetically-trapped \sp7Li vapor was experimentally observed and quantitative measurements of condensate number were made. Compared to other BEC experiments, lithium is unique due to its negative s-wave scattering length, corresponding to effectively attractive interactions. Due to this attraction, condensates are expected to undergo mechanical collapse if the condensate number exceeds a critical value. In this experiment, an upper limit of about 1000 condensate atoms is found, in agreement with theoretical predictions. In the experiment, the atoms are confined by a set of six permanent magnets in the Ioffe configuration. Optical forces are used to slow and guide atoms from a thermal atomic beam into the magnetic trap. With about 10\sp8 atoms loaded into the trap, the vapor is laser-cooled to near 200 μK and then evaporatively cooled by application of a resonantly-tuned microwave field. Evaporative cooling produces a million-fold increase in phase-space density, reaching quantum-degenerate conditions with about 10\sp5 atoms at temperatures near 300 μK. After cooling, the trapped atom distribution is observed by in situ imaging via an optical probe. Calculated atom distributions are fit to the image data. In initial data, the imaging resolution was insufficient to see the spatially-narrow condensate peak, but as phase-space densities approached the expected phase transition, the images suddenly became distorted. Initial fits to the data suggested as many as 10\sp5 condensate atoms, in strong disagreement with theoretical predictions. An imaging model, accounting for imperfections in the imaging optics, shows that the sudden appearance of the distortions is a consequence of BEC, and that these distortions led to the initial over-estimation of cloud phase-space density and condensate number. Improved imaging was obtained using large probe detunings, a Phase-Contrast Polarization Imaging (PCPI) technique, and near-diffraction-limited imaging optics. The PCPI method exploits the birefringence of the trapped atoms. From the resulting images, quantitative estimates of condensate number are obtained and compared with theory.