The Local Group is an excellent laboratory for studies of galaxy evolution at the highest possible resolution in that it provides us with a wide range of different galaxy types and a variety of environments. Yet the Local Group is a poor group, contains relatively few galaxies, and lacks very massive galaxies, such as large ellipticals. Similar to many other nearby groups, the mass and the luminosity of the Local Group are dominated by two large spirals, the Milky Way and M31. Most of the other Local Group members are dwarf galaxies, and the majority of them are found in close proximity to the two large spirals.
Dwarf galaxies are often considered building blocks of more massive galaxies in models of hierarchical structure formation. Dwarf galaxies come in many different flavors and cover a range of masses, luminosities, morphologies, gas content, star formation histories, etc. The distinction between dwarf galaxies and larger galaxies is somewhat fuzzy. The difference is primarily a luminosity difference - it is customary to call galaxies with absolute magnitudes of MV > -18 dwarf galaxies. Gas-rich dwarfs include dwarf spirals, dwarf irregulars (dIrrs) and blue compact dwarf galaxies, which usually show differing levels of ongoing star formation. Gas-poor dwarfs are primarily dwarf ellipticals (dEs). These can be further subdivided into subtypes such as the more massive, strongly centrally concentrated dwarf ellipticals with higher surface brightness, and the less massive, faint, fairly diffuse dwarf spheroidals (dSphs) (see also Gallagher & Wyse 1994; Grebel, Gallagher, & Harbeck 2003).
What makes the Local Group special (apart from its being our home) is that here we have the possibility to actually resolve its constituent galaxies into individual stars and to study the properties of these stars. We can use these stars as probes of the past - they permit us to uncover the evolutionary histories of their host galaxies. Moreover, they permit us to study these evolutionary histories at a level of detail and accuracy that is unmatched by any more distant galaxy, where only the integrated light can be studied. The Local Group is the only place where we can analyze even ancient stars and uncover the early formation history of individual galaxies beyond our own, particularly of the dwarf companions of the Milky Way. To summarize, the Local Group is ideally suited for studies of "near-field cosmology", i.e., for studies of galaxy evolution over cosmological epochs based on their resolved stellar fossil record, and for tests of the corresponding cosmological models.