I come from Poland, but I found this website (I don't remember how), and I used the applet with explanation about 2D collision to understand this situation. The problem is, I cannot figure what happens and how to calculate the velocities of more colliding balls when they hit each other at the same time. I could predict, what would happen, but is not exact calculation, but my guess. Moreover, google didn't help me in finding information about that. I am trying to write my own simple billiard game, and the most difficult task to understand is the physics.

So could you please explain me (or at least post some links to such explanation) what happens when many balls collide?

Every ball has its mass (m), velocity (Vx, Vy), coordinates (x,y). The radius is constant, identical for every ball. Example for such situation:
3 balls with radius 10:
-x=0, y=100, Vx=20, Vy=0, m=1
-x=100, y=90, Vx=0, Vy=0, m=1
-x=100, y=110, Vx=0, Vy=0, m=1

With regards