The Principle of the Conservation of Momentum states that:
if objects collide, the total momentum before the collision is the same
as the total momentum after the collision (provided that no external
forces - for example, friction - act on the system).
That's amazingly useful because it means that you can tell what is going to happen after a collision before it has taken place.
Principle of Conservation of Energy: Of course,
energy is also conserved in any collision, but it isn't always conserved
in the form of kinetic energy, so be careful.