Trackmania Nations is a free racing game for Windows that distinguishes itself from normal racing games by introducing a number of additional elements to the tracks. Do you remember Stunt Car Racer for instance ? The game where you were driving through loopings and made big jumps across the screen.
This game introduces all those elements again to a racing game but provides normal tracks as well. You may start with the 90 solo missions that remind me a little bit of the Gran Turismo missions. They are divided into Beginner, Advanced and Expert Training missions and award medals if you beat the tracks in a certain amount of time. This alone is very challenging.

