There's an introduction available in-game, which explains the basics :

Red cores launch a homing missile towards the nearlest leech. Every 10th core launches a spray of missiles that travel in a straight line from your position.
Blue cores shield you against leeches and enemy missiles (but not against bosses!) for a short while. Every 10th core heals one heart.
Yellow cores increase your speed for a short while. Every 10th core slows down both leeches and bosses for a short while.

Four basic missions (easy difficulty) are available from the start, if you complete any of these missions, a more difficulty version of it becomes unlocked. There are 3 difficulty modes (easy - normal - hard). Completing two out of the 4 basic missions within the same difficulty unlocks the 'Endless' mission, completing all 4 basic missions within the same difficulty unlocks the 'Boss' mission for that difficulty.

Collect : collect a number of crystal cores of each color.
Survive : survive a certain amount of time.
Charge : charge 3 crystal towers up to a certain level.
Swarm : survive several swarms of leeches - crystal towers are present to help you.

Endless : never-ending survival mode.

Boss : 3 different bosses have to be defeated - each difficulty has its own boss.

Pages on the NULLL forum :
Crystal Chaos forum.

Wiki pages:
Main Page
Screenshots & more