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High-resolution images of the disks of NGC 4038/39 obtained with the HST \ \ Wide Field Camera are presented. NGC 4038/39 is a prototypical example of a pair of colliding galaxies thought to be at an early stage of a merger. Down to the limiting magnitude of $V \approx 23$, the HST images reveal a population of over 700 blue pointlike objects within the disks. The mean absolute magnitude of these objects is $M_V$~= $-$11, with the brightest objects reaching $M_V$~$\approx$ $-$15 ($H_0$~= 50). Their mean apparent color indices are $U\!-\!V$~= $-$0.8 and $V\!-\!I$~= $+$0.8, while their mean indices corrected for internal reddening are $(U\!-\!V)_0$~= $-$1.1 and $(V\!-\!I)_0$~= $+$0.5. Their mean effective radius, determined from slightly resolved images, is 18 pc. Based on their luminosities and resolution, most of these objects cannot be individual stars, but are likely young compact star clusters. The brighter ones are similar to the NGC 1275 and NGC 7252 clusters that appear to be young globulars formed during recent galaxy mergers. Based on their $UVI$ colors, the brightest, bluest clusters of NGC 4038/39 appear to be $<$10 Myr old. Most of these bright clusters are relatively tightly clustered themselves, with typically a dozen individual clusters belonging to a complex identified as a giant HII region from ground-based observations. The cluster luminosity function (LF) is approximately a power law, $\phi(L)dL \propto L^{-1.78 \pm 0.05} dL$, with no hint of a turnover at fainter magnitudes. In shape this power law agrees with the LF of Magellanic Cloud clusters and Galactic open clusters, but differs from the LF of old globular cluster systems that is typically Gaussian with a FWHM of $\sim$3 mag. We shall discuss various possible explanations for this apparent difference.
