Players represent alien races that are seeking to spread themselves onto five foreign worlds. To accomplish this, they make challenges against other players and enlist the aid of interested parties. But alien powers, which are unique to each race, give players ways to bend or outright break some rule in the game.

This is an updated version of the original Eon Cosmic Encounter (1977).

Major differences between this version and the Eon version:

• Flares in the Mayfair version are "use once and discard", as opposed to Eon's version, which lets players reuse them.
• Moons (in the More Cosmic Encounter expansion) have text written on them (instead of only a number which you used to refer to a separate list). Moons also were divided into four categories: Full Moons have a major effect on the game; Half Moons are more moderate in their effects; Quarter Moons have a minor effect; Cheese Moons introduce silliness to the game.
• Lucre (in the More Cosmic Encounter expansion) was revamped with additional uses, and players were required to spend it to affect their challenge totals.
• Mayfair introduced a new card: Reinforcements, as well as new Edicts, and several new Alien Powers with corresponding Flares.
• Mayfair introduced phase / timing icons on all Powers, Flares, and Edicts to clearly indicate when each could be used.

Expanded by:

• More Cosmic Encounter