Conquest is a strategic space exploration and conquest (naturally) game for 2-4 players. Each player starts in a system at a corner of the map and expands outward from there.
Each player represents a different spacefaring race/organization - the Terrans, the Olso Empire, the Federation (changed to the Confederation in the second edition), and the Tholians (changed to the Lothians in the second edition). Each has a different set of units they can build, with varying capabilities - ships are rated for space combat, ground (bombardment) combat, drive system, and what kind of damage they take from the various combat results.
When a star is explored a card is drawn which determines the class of the inhabitable world found there and, if inhabited, its attitude to each of the players. In addition to the attitude the value of each kind of planet varies by player.
There are three different long-range movement systems in the game - warp drive, jump drive (similar to warp drive but much less accurate), and stargates, which have to be built and carried to where you want to use them. Each player uses one of the three systems for their ships.
The second edition, in addition to changing the names of two of the races, changed some of the ship designs which were similar to Star Trek and Star Wars ships. It also changed the name of the game to The Conquest and Exploration of Space.