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The galaxy census of the Local Group remains uncertain. Within the Local Group's volume as defined by its zero velocity surface of ~ 1 Mpc (Karachentsev et al. 2002), we currently know of some 38 probable member galaxies. Some were only recently discovered, and additional faint candidates continue to be found (e.g., Zucker et al. 2004a, b). All of the newly discovered dwarfs are dSphs, the least massive, least luminous galaxies known, and thus contribute to the faint end of the galaxy luminosity function. For reviews on Local Group dwarfs, see, e.g., Grebel (1997, 1999, 2000, 2001, 2005), Mateo (1998), and van den Bergh (1999, 2000).

DSphs are usually the most numerous type of galaxy in galaxy groups and are characterized by MV < -14 mag, µV < 22 mag arcsec-2, MHI < 105 Modot, and Mtot ~ 107 Modot. Often their stellar populations are purely old, but mixtures of old and intermediate-age populations are found as well. In dSphs where several populations can be distinguished the younger and/or more metal-rich populations are more centrally concentrated, indicating extended star formation episodes in the centers of the shallow potential wells of their parent galaxies (Harbeck et al. 2001). The gas deficiency of dSphs remains an unsolved puzzle - dSphs typically contain even less gas than expected from red giant mass loss over time scales of several Gyr. The metallicity-luminosity relations of dSphs and dIrrs show the usual trend of increasing metallicity with increasing galaxy luminosity, but the relations are offset from each other: DSphs have higher mean stellar metallicities at a given optical luminosity, which may indicate more rapid star formation and enrichment at early times as compared to dIrrs (Grebel et al. 2003).

DSphs do not seem to be supported by rotation and appear to contain large amounts of dark matter. The latter is inferred from the high velocity dispersion and the resulting high mass-to-light ratios derived under the assumption of virial equilibrium. Indirectly, a high dark matter content is also supported by the morphology of some nearby dSphs (Odenkirchen et al. 2001) and by the observed lack of a significant depth extent (Klessen, Grebel, & Harbeck 2003). The radial velocity dispersion profiles of dSphs fall off large radii (Wilkinson et al. 2004), possibly indicating the presence of a kinematically cold stellar population at the outermost radii.

If dwarf galaxies in general and dSphs in particular are indeed building blocks of larger galaxies, then today's dwarf population may be considered to be the surviving population of satellites that has not yet been accreted. The most numerous type of dwarfs in galaxy groups, the dSphs, may then be the most pristine members of the original building block population. Studying dSphs may teach us about the properties of objects that presumably were once accreted in large numbers to form galaxies like the Milky Way. Alternatively, it is conceivable that dSphs are in fact not fossil building blocks, but stripped remnants of disrupted and originally much more massive galaxies that have since merged. To find out more about the nature of dSphs and their cosmological significance we need to understand their past and present-day properties.

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