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We have analyzed Hubble Space Telescope (HST) images of the compact, luminous star cluster R136 in the LMC that were taken with the refurbished HST and new Wide Field/Planetary Camera. These images allow us to examine the stellar population in a region of unusually intense star formation at a scale of 0.01 pc. We have detected stars to 23.5 in F555W and have quantified the stellar population to an M<SUB>555,0</SUB> of 0.9 or a mass of 2.8 M<SUB>sun</SUB>. Comparisons of HR diagrams with isochrones that were constructed for the HST flight filter system from theoretical stellar evolutionary tracks reveal massive stars, a main sequence to at least 2.8 M<SUB>sun</SUB>, and stars with M<SUB>555,0</SUB> ≥ 0.5 still on pre-main sequence tracks. The average stellar population is fit with a 3-4 Myr isochrone. Contrary to expectations from star formation models, however, the formation period for the massive stars and lower mass stars appear to largely overlap. We have measured the IMF for stars 2.8-15 M<SUB>sun</SUB> in three annuli from 0.5-4.7 pc from the center of the cluster. The slopes of the IMF in all three annuli are the same within the uncertainties, thus, showing no evidence for mass segregation beyond 0.5 pc. Furthermore, the combined IMF slope, -122±006 is close to a normal Salpeter IMF. The lower mass limit must be lower than the limits of our measurements: ≤ 2.8 M<SUB>sun</SUB> beyond 0.5 pc and ≤ 7 M<SUB>sun</SUB> within 0.1 pc. This is contrary to some predictions that the lower mass limit could be as high as 10 M<SUB>sun</SUB> in regions of intense massive star formation. Integrated properties of R136 are consistent with its being comparable to a rather small globular cluster when such clusters were the same age as R136. From the surface brightness profile, an upper limit for the core radius of 0.02 pc is set. Within a radius of 0.4 pc we estimate that there have been roughly 20 crossing times and relaxation should be well along. Within 0.5 pc crowding prevents us from detecting the intermediate mass population, but there is a hint of an excess of stars brighter than M<SUB>555,0</SUB> = -5 and of a deficit in the highest mass stars between 0.6 pc and 1.2 pc. This would be consistent with dynamical segregation.