I have trouble while detecting collisions on my 3D-Game.

I have set-up Rays, to detect collisions (Screenshot) and my main-rountine already analyzes them. But now there's the question what to do with that.

One possibility would be, to move the player back to the last position, but that's dirty, and does not work if the player can walk in multiple directions (e.g. if the player runs along a wall).

My question is, what to do with the collision data / or in which direction, by which amount move the player? I'm sure there is an algorithm for that (as for almost all is).