The Alpha Quadrant is the designation for one-quarter of the galaxy, adjacent to the Beta Quadrant and the Gamma Quadrant. The designation originated with the United Federation of Planets, who defined the Sol System as the border between the Alpha and Beta Quadrants. Half of Federation territory lies in the Alpha Quadrant, with the Cardassian Union and the Tholian Assembly as the two next large and powerful governments. The Federation has explored less than half of the quadrant, though much of this space consists of the distant galactic rim.
It is worth noting that the collective powers of the Alpha and Beta Quadrant have often been colloquially referred to solely as the 'Alpha Quadrant,' most notably in engagements with the Dominion of the Gamma Quadrant. Such a colloquial term has historically referred to the geopolitical landscape of the Federation, the Klingon Empire, the Old Romulan Star Empire, and sometimes the Cardassian Union, as intersecting powers exerting influence on one another.