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HST has now imaged upwards of 50 galactic nuclei. The sample divides into two broad categories: early-type bulges/ellipticals, and spirals. Early-type nuclei tend to follow broad trends foreshadowed by earlier ground-based data, but with some important differences. Large early-type galaxies show ``break radii" that are analogous to classical core radii. However, inside these cores, most light profiles do not level out but continue to increase in shallow power laws inwards to the resolution limit (0.1\arcsec). We call such nuclei ``soft cores." Small early-type galaxies are completely unresolved and show steep power-laws at all radii. We call these ``hard cores." Early-type galaxies of intermediate brightness seem to be divided into hard cores or soft cores according to rotation and isophote shape: rotating, disky E's have hard, steep cores, while non-rotating, boxy E's have soft cores and breaks. Thus, core properties seem to reinforce the division of ellipticals into two fundamentally different families that has been emerging for some time now based on other data.
Core phase-space density shows an enormous range in early-type galaxies, decreasing by a factor of 100 million from the smallest ellipticals to the largest. Since phase-space density is believed to either remain constant or increase during mergers, this trend casts doubt on whether large E's could have formed by merging from progenitors that looked like present-day small E's. The smallest and closest elliptical, M32, is so dense that stellar collisions have likely been important over the age of the Universe. M32's relatively high stellar velocity dispersion ($\sim 100$ km s$^{-1}$) favors runaway merging in collisions to form a black hole. Evidence for such a BH has been found from ground-based spectroscopy.
Compared to early-type galaxies, spiral nuclei show a wider range of morphologies and physical phenomena, some quite exotic. Nuclear star clusters are common in spirals. The density is so high in the nearby star-cluster nucleus of M33 that stars appear to be colliding and merging to make massive O, and B stars. In contrast to M32, M33's lower velocity dispersion does not favor formation of a black hole but rather indicates a classic core bounce, as in globular clusters. The nucleus of M31 is perhaps the biggest dynamical puzzle so far. It contains a double star cluster separated by 1.5 pc, each one possibly with its own BH (based on ground-based spectroscopy). In M31 we may be witnessing the remnant nucleus of a former galactic merger victim of M31, which has spiralled to the center via dynamical friction. However, the dynamical lifetime of such a double cluster to merging is only $\sim 10^6$ yr, so catching the system at just this point in its evolution would seem improbable. A satisfactory theory for this interesting system is so far lacking.
Galactic cores as viewed by HST are proving to be fascinating laboratories for pushing the envelope of stellar dynamics and constraining theories of galaxy evolution in new and unsuspected ways. This review is based on work done jointly with Tod Lauer, Carl Grillmair, John Kormendy, Yong Byun, Alan Dressler, Douglas Richstone, Scott Tremaine, and members of the Wide-Field/Planetary Camera Team, to whom sincere thanks and appreciation are extended.
