THE GALAXY  
Our Galaxy is divided into four quadrants: Alpha, Beta, Gamma and Delta. The Galaxy is almost 100,000 light years in diameter, and at its central bulge is about 10,000 light years across. It is because of this size it was divided into the four quadrants. 

ALPHA QUADRANT  
This quadrant is home to most of the worlds that belong to the United Federation of Planets, including Earth, which lies on the perimeter between the Alpha and Beta quadrants. Some of the Federation member worlds also reside within the Beta Quadrant. Even though Federation space lies within this quadrant, galactic space is so vast that even most parts of the Alpha Quadrant remain uncharted and unexplored by Starfleet. The Bajoran space station Deep Space Nine is also located in the Alpha Quadrant. The stable Bajoran Wormhole in the nearby Denorios Belt has a terminus in the Gamma Quadrant, and has given the Federation a gateway into that part of the Galaxy. The Alpha Quadrant is also the home of the Cardassian Union.

BETA QUADRANT 
Some parts of the United Federation of Planets fall within the Beta Quadrant. But Federation exploration of this part of space has been limited, because both the Klingon and Romulan empires are located in the quadrant. It is not known exactly how far the Klingon and Romulan empires extend, but it seems certain that the vast majority of the Beta Quadrant remains unexplored and may well be that way for a lot longer. 
 
 
 
DELTA QUADRANT 
Very little is known about this quadrant. Like the Gamma Quadrant, it is tens of thousands of light years from Federation space. The Borg Collective home world is believed to lie in the Delta Quadrant. The Barzan Wormhole, which had been believed to be stable, had one terminus in the Delta Quadrant, but that end-point was discovered to move unpredictably, and could now be located anywhere in the Galaxy. The Starship U.S.S. Voyager NCC-74656 was transported to the Delta Quadrant by the being know as The Caretaker. It is currently the only known Federation vessel to be traveling through that part of the Galaxy.
GAMMA QUADRANT 
This is the part of the Galaxy that is most remote from the United 
Federation of Planets, and at its closest point it lies 40,000 light 
years from Federation space. In 2369, a stable wormhole was 
discovered in the Denorios Belt, close to the the planet Bajor. The Bajoran Wormhole provides a nearly instantaneous gateway into the Gamma Quadrant, eliminating what would normally be a 60 year journey at warp nine, and enabling exploration of that region of space.The Dominion appears to control large areas of the Gamma Quadrant and because of the Bajoran wormhole, now poses a threat to the worlds of the Alpha Quadrant.
  
Wormholes are the only practical means of traveling across vast amounts of space. But most are unstable. The only stable wormhole found as yet is the Bajoran Wormhole.