The single player "story" mode is senseless and plays exactly like the multiplayer side, except you're playing against bots.
Multiplayer, though, was pretty cool. Four-player deathmatch mode was great fun. I'm a little bummed that the PS2 analog sticks weren't sensitive enough to handle fine-tuned aiming . . . but other than that, it was good stuff.
TimeSplitters has a cool level editing tool that (besides taking up nearly all available space on your standard memory card), was really deep and allowed players to make their own multiplayer levels. More console games should do this.
Game Title: TimeSplitters
Platform: PlayStation 2
Genre: First Person Shooter
Developer: Free Radical
Release Date: 23rd Oct 2000