  Galaxy cluster mass distribution are potentially useful probes of $\Omega_0$
and the nature of the dark matter. Large clusters will distort the observed
shapes of background galaxies through gravitational lensing allowing the
measurement of the cluster mass distributions. In this paper we describe weak
statistical lensing measurements of the most luminous X-ray cluster known,
RXJ1347.5-1145 at z=0.45. We detect a shear signal in the background galaxies
at a signal-to-noise ratio of 7.5 in the radial range $120 \le r \le 1360
h^{-1}$ kpc. A mass map of the cluster reveals an 11$\sigma$ peak in the
cluster mass distribution consistent with the position of the central dominant
galaxy and 3 $\sigma$ evidence for the presence of a subcluster at a projected
radius of 1.3 - 1.7 h^{-1} Mpc from the cluster center. In the range $120 \le r
\le 1360 h^{-1}$ kpc mass traces light, and the azimuthally averaged cluster
mass and light profiles are consistent with singular isothermal spheres with
M(r<1 Mpc) = $1.7 \pm 0.4 \times 10^{15} M_\odot$. Assuming an isotropic
velocity distribution function, the implied velocity dispersion is $\sigma =
1500 \pm 160 km s^{-1}$. The rest-frame mass-to-light ratio is $M/L_B = 200 \pm
50 h M_\odot/L_{B\odot}$. The lensing mass estimate is almost twice as high as
a previously determined X-ray mass estimate.
