Local Galaxy Group
The Local Group consists of two giant spiral galaxies; the Milky Way and the Andromeda Galaxy; a few medium sized galaxies; M33, Large Magellanic Cloud, and Small Magellanic Cloud; and approximately forty dwarf galaxies. The total number is not known because some small dwarf galaxies may be so faint that they have not been detected yet, but mainly because a large part of the sky is covered by our own galaxy and there may be a number of galaxies, even large ones, lurking behind the dust and gas clouds of the Milky Way.
Of the Local Group, our Milky Way and Andromeda are by far the most massive. The two closest galaxies to the Milky Way are called the Magellanic Clouds, which may be viewed as satellite galaxies to the Milky Way at a distance of a little less than 200,000 light years. They are only visible in the Southern Hemisphere, but can easily be seen by the naked-eye and their brightest stars can be seen with binoculars. They are irregular galaxies and are much smaller than the Milky Way.
The LMC and SMC
The Large Magellanic Cloud, together with its apparent neighbor and relative, the Small Magellanic Cloud, are conspicuous objects in the southern hemisphere, looking like separated pieces of the Milky Way for the naked eye. They were certainly known since the earliest times by the ancient southerners, but these people produced little documents which are still preserved. Both Magellanic Clouds are irregular dwarf galaxies orbiting our Milky Way galaxy, and thus are members of our Local Group of galaxies. The Large Magellanic Cloud, at its distance of 179,000 light years, was longly considered the nearest external galaxy, until in 1994, the Sagittarius Dwarf Elliptical Galaxy was discovered at only about 80,000 light years.
Galaxy groups stay together as groups, and are defined as groups, due to the gravitational interaction, i.e. dynamics, they impose on each other. Usually a group has two or three massive galaxies that dominate the dynamics of the group and a variety of smaller galaxies which more or less orbit the massive ones or are exchanged between them, or in some cases are flung out of the system altogether when they fly close to a massive galaxy. It is also possible that the massive one devours a dwarf galaxy that comes too close.
Sometimes other nearby groups are included in the Local Group and then we talk about the Extended Local Group of Galaxies. These other groups may have played an important role in the Local Group dynamics, or may still do so.