Timesplitters 4? There was a 1, 2, and 3???
Must be a very relevant game in the industry.
TS2 and 3 (Timesplitters 3 is usually called Timesplitters: Future Perfect) are brilliant. TS1 is mainly a multiplayer game, with a mapmaker, some challenges and a single player campaign that's tacked into the multiplayer levels.
Timesplitters 2 was much better, with a proper single player campaign (i.e. it had levels designed purely for single player, it didn't use multiplayer levels for single player), co-op mode, challenges, lots of options for multiplayer, and a stack of unlockables.
Timesplitters 3 is probably my favourite game of the last console generation; it has a much better single player campaign than TS2, a better mapmaker, and 150 different characters you could play as or against in multiplayer, most of whom needed to be unlocked.
In all three games, you could play against bots in all multiplayer modes, even on the maps you'd made yourself. The mapmaker was very easy to use, though of course is massively limited when compared to the mapmakers you get with games like Unreal Tournament and Half-Life (it's swings and roundabouts - the Timsplitters mapmakers are very easy to use, but have relatively few options, it's very quick to make and test your maps, whereas on a PC game like UT or Quake 3, the mapmakers (called editors, usually) are far more complex but can create a map *exactly* how you want it to be, as long as you have sufficient skill and time to create the map).
TS2 and 3 are classics, I don't much like TS1, but some people did really like it, and maybe still do. I probably prefer TS3 to any FPS made after it, even Bioshock or Singularity.