We present UBVRI and Hα photometry of the extremely compact, starburst cluster NGC 3603. Ground-based images, Hubble Space Telescope (HST) archival data, as well as Chandra X-ray data have been used for this study. We present, for the first time, optical color-magnitude diagrams (CMDs) for the stars in the cluster core down to V=22 mag. A well-defined main sequence (MS) as well as low-mass pre-main-sequence (PMS) stars can clearly be seen in the CMDs. This result confirms the finding by Eisenhauer et al. that low-mass stars are forming in the starburst cluster. We also derive an age (1+/-1 Myr) and distance of the cluster (V0-MV=14.2+/-0.2 mag, i.e., d=6.9+/-0.6 kpc). The interstellar reddening shows a minimum value [E(B-V)=1.25 mag] at the core (r<=0.2′) and increases rapidly up to E(B-V)~1.8 mag or even higher with increasing distance from the center, which suggests the presence of a wind-driven cavity near the cluster center as found by Frogel et al. and Clayton. We also determine the radius of the cluster (r~2') from the surface-density profile of bright stars and X-ray sources. To investigate the initial mass function (IMF) of the cluster, we performed a completeness test for the core region. Using the theoretical mass-luminosity relation of MS as well as PMS stars, we derived the IMF of stars imaged with the HST/PC1. The surface density of stars in the core is enormously high and decreases gradually with increasing distance from the center. The slope of the IMF also shows radial variation: fairly flat in the core (Γ=-0.5+/-0.1 at r<=0.1′) and gradually steepening (Γ=-0.8+/-0.2 at r=0.1′~0.2′ and Γ=-1.2+/-0.2 at r>0.2′ of HST/PC1). The stars in the halo region of NGC 3603 (outside of HST/PC1) seem to be slightly older (age~5 Myr) and presumably formed before the stars in the core.