What is a Galaxy

A galaxy is a vast, gravitationally bound collection of billions of stars and their associated "friends." 

Their "friends" include nebulae, stellar remnants, planets and a whole host of other smaller particles including the basic elements hydrogen and helium. Galaxies also consist of an important but poorly understood substance called dark matter. It is believed to surround every galaxy and accounts for much of its mass. 

Galaxies vary in size and shape. They range from dwarfs that may only consist of a few million stars to giants that can have trillions of them, all orbiting a center of mass. Galaxies are categorized based on their apparent shapes. Elliptical galaxies are bright, featureless spheroids consisting mostly of old, low-mass stars. Spiral galaxies are disk shaped and have a variety of stars, and irregular galaxies are a catch-all for those with no distinct shape. 

Many galaxies, including the Milky Way, orbit around what is to believed to be a supermassive black hole; smaller than a pinhead but with the mass of millions or billions of Suns. The supermassive black hole in the center of our galaxy flattens it into a disk with a depth of a few light years whereas the diameter is about 100,000 light years. 

It is estimated that there are between 100-300 billion galaxies in the observable Universe! Check out the links below for more information and to see some cool pictures of different galaxies.
I think you mean galaxy. A galaxy is a large group of stars that are held together by gravitation or gravity. We live in the Milky Way Galaxy. There are MILLIONS if stars, and also the universe is expanding every possible day. So know one knows how many galaxies there are.

"A galaxy is, by definition, any large collection of stars that can be recognized as a distinct physical entity. In terms of the number of stars, a small 'dwarf irregular' galaxy like the Small Magellanic Cloud, has about one billion stars in it, but there are even smaller systems that are recognized as galaxies such as the Leo I and II dwarf galaxies with about 1 million stars in them, and the Draco System with a few hundred thousand stars in it. The largest star cluster, a globular cluster called Messier 15 has about 6 million stars, so we see that for small galaxies, there is a blurring together of what we mean by a galaxy and a large star cluster. In addition to their mass and numbers of stars, a galaxy is a collection of stars and gas which move through the universe independently of the Milky Way. Globular clusters are roundish swarms of stars that orbit the Milky Way, while the Leo and Draco Systems seem to be independent collections of stars.

Many galaxies also continue to form new generations of stars. The Milky Way, and all spiral shaped galaxies like it (see above image of NGC 2997), produce new stars at a rate of one or two stars per year. These stars are formed in the vast interstellar clouds that account for about 1 to 10 percent of the mass of these galaxies. Globular star clusters, on the other hand, are not currently forming stars because this activity happened billions of years ago and then stopped once all of the gas and dust clouds were used up.

Our galaxy, the Milky Way, is typical: it has hundreds of billions of stars, enough gas and dust to make billions more stars, and at least ten times as much dark matter as all the stars and gas put together. And it’s all held together bygravity.

Like more than two-thirds of the known galaxies, the Milky Way has a spiral shape. At the center of the spiral, a lot of energy and, occasionally, vivid flares. are being generated. Based on the immense gravity that would be required explain the movement of stars and the energy expelled, the astronomers conclude that the center of the Milky Way is a supermassive black hole.

Other galaxies have elliptical shapes, and a few have unusual shapes like toothpicks or rings. The Hubble Ultra Deep Field (HUDF) shows this diversity. Hubble observed a tiny patch of sky (one-tenth the diameter of the moon) for one million seconds (11.6 days) and found approximately 10,000 galaxies, of all sizes, shapes, and colors. From the ground, we see very little in this spot, which is in the constellation Fornax.

Formation

After the Big Bang, the Universe was composed of radiation and subatomic particles. What happened next is up for debate - did small particles slowly team up and gradually form stars, star clusters, and eventually galaxies? Or did the Universe first organize as immense clumps of matter that later subdivided into galaxies?

Collisions

The   Shapes of Galaxies are influenced by their neighbors, and, often,Galaxies  Collide  The Milky Way is itself on a   Collison Course with our nearest neighbor, the Andromeda galaxy. Even though it is the same age as the Milky Way, Hubble observations reveal that the stars in Andromeda's halo are much younger than those in the Milky Way. From this and other evidence, astronomers infer that Andromeda has already smashed into at least one and maybe several other galaxies.

For More Info:NASA SCIENCE   -http://science.nasa.gov/