We present an optical analysis of 55 members of R136, the central cluster in the Tarantula Nebula of the Large Magellanic Cloud. Our sample was observed with STIS aboard the Hubble Space Telescope, is complete down to about 40 M☉, and includes seven very massive stars with masses over 100 M☉. We performed a spectroscopic analysis to derive their physical properties. Using evolutionary models, we find that the initial mass function of massive stars in R136 is suggestive of being top-heavy with a power-law exponent γ ≍ 2 ± 0.3, but steeper exponents cannot be excluded. The age of R136 lies between 1 and 2 Myr with a median age of around 1.6 Myr. Stars more luminous than log L/L☉ = 6.3 are helium enriched and their evolution is dominated by mass-loss, but rotational mixing or some other form of mixing could be still required to explain the helium composition at the surface. Stars more massive than 40 M☉ have larger spectroscopic than evolutionary masses. The slope of the wind-luminosity relation assuming unclumped stellar winds is 2.41 ± 0.13 which is steeper than usually obtained (∼1.8). The ionizing ( $\log Q_0\, [{\rm ph/s}] = 51.4$ ) and mechanical ( $\log L_{\rm SW}\, [{\rm erg/s}] = 39.1$ ) output of R136 is dominated by the most massive stars ( $\gt 100\, \mathrm{ M}_{\odot }$ ). R136 contributes around a quarter of the ionizing flux and around a fifth of the mechanical feedback to the overall budget of the Tarantula Nebula. For a census of massive stars of the Tarantula Nebula region, we combined our results with the VLT-FLAMES Tarantula Survey plus other spectroscopic studies. We observe a lack of evolved Wolf-Rayet stars and luminous blue and red supergiants.