We report 0.15" resolution near-infrared (NIR) imaging of R136, the central region of 30 Doradus in the Large Magellanic Cloud. Our 12.8"x12.8" images were recorded with the MPE camera SHARP II at the 3.6m ESO telescope, using the adaptive optics system COME ON+. The high spatial resolution and sensitivity (20th magnitude in K) of our observations allow our H- and K-band images to be compared and combined with recent Hubble Space Telescope (HST) WFPC2 data of R136. We fit theoretical models with variable foreground extinction to the observed magnitudes of ~1000 stars (roughly half of which were detected in HST and NIR bands) and derive the stellar population in this starburst region. We find no red giants or supergiants; however, we detect ~110 extremely red sources which are probably young, pre-main-sequence low- or intermediate-mass stars. We obtained narrow-band images to identify known and new Wolf-Rayet stars by their He II (2.189um) and BrGamma (2.166um) emission lines. The presence of W-R stars and absence of red supergiants narrow the cluster age to 3-5Myr, while the derived ratio of W-R to O stars of 0.05 in the central region favors an age of ~3.5Myr, with a relatively short starburst duration. For the O stars, the core radius is found to be 0.1pc and appears to decrease with increasing stellar mass. The slope of the mass function is Gamma=-1.6 on average, but it steepens with increasing distance from the cluster center from Gamma=-1.3 in the inner 0.4pc to Gamma=-2.2 outside 0.8pc for stars more massive than 12 Msun. The radial variation of the mass function reveals strong mass segregation that is probably due to the cluster's dynamical evolution.