  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\,$M_{\odot}$, and includes 7 very massive stars with masses over
100\,$M_{\odot}$. We performed a spectroscopic analysis to derive their
physical properties. Using evolutionary models we find that the initial mass
function (IMF) of massive stars in R136 is suggestive of being top-heavy with a
power-law exponent $\gamma \approx 2 \pm 0.3$, 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 $\log L/L_{\odot} = 6.3$ 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\,$M_{\odot}$ have larger
spectroscopic than evolutionary masses. The slope of the wind-luminosity
relation assuming unclumped stellar winds is $2.41\pm0.13$ which is steeper
than usually obtained ($\sim 1.8$). The ionising ($\log Q_0\,[{\rm ph/s}] =
51.4$) and mechanical ($\log L_{\rm SW}\,[{\rm erg/s}] = 39.1$) output of R136
is dominated by the most massive stars ($>100\,M_{\odot}$). R136 contributes
around a quarter of the ionising 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.
