Our galaxy, the Milky Way is one member of a nearby group of about 40 known galaxies, called the Local Group. The true number remains unknown as the census has steadily grown over the years as new members become identified. The Local Group contains members of most galaxy types including large spirals like the Milky Way, M31, and M33. It also contains several bright irregular galaxies (the Magellanic clouds), several dim Irregulars, several Dwarf galaxies (nucleated, spheroidal, elliptical, compact types), and even a highly stripped galaxy (Sagittarius DEG). The only important type not represented in the Local Group, is the Elliptical type. The decision to include a galaxy within the Local Group is not straight forward. The best criterion is dynamical, in that the galaxy should be gravitationally bound to the other Local Group galaxies. To simplify matters the radius of the Local Group has been established to about one million parsecs (3.26 million light years) and all galaxies within that radius are said to belong to the Local Group.
Because of its proximity, the Local group represents a unique opportunity for astronomers to study galaxy evolution in the greatest possible detail. Galaxies evolve by two primary methods. The first is dynamical, through the hierarchical acquisition of external systems (mostly Dwarf galaxies) into the basic structure of the galaxy. The second is internal, through the formation, life, and death of stars within the galaxy.
The Local Group's dominant galaxies, M31 and the Milky Way have each acquired a system of satellite galaxies. For instance the Milky Way has accumulated a system of Dwarf galaxies such as the Magellanic Clouds and the Sag DEG, to name a few. The Milky Way probably has at least a dozen satellite galaxies in total spread across the sky including one which is actively being consumed by our galaxy, the Sagittarius Dwarf Elliptical galaxy. Andromeda (M31) has two well known bright companions, M110 and M32 in addition to several other lesser known satellite Dwarf galaxies. There are other members, mostly Dwarf galaxies which cannot be assigned to any particular subgroup and seem to float alone in the Local Group.
The two giants galaxies of the Local Group, the Milky Way and the Andromeda Galaxy, are in orbit around each other and comprise at least 50% of the total mass of the Local Group galaxies. The gravitational center of the Local Group lies somewhere between the two giant spirals and some astronomers believe the two may ultimately merge in the distant future to form a giant elliptical galaxy. There is some evidence that the third largest member, M33, may be an outlying gravitationally bound companion of M31. The Local Group galaxies do not represent an entirely isolated system but almost certainly interact and exchange members with other nearby groups such as the Maffei 1 group, the Sculptor group, the M81 group, and the M83 group.