AssaultCube, Nexuiz, Tremulous, Sauerbraten:
AssaultCube – the regular repos have an outdated client; you can only play single player.I discovered by accident that if you add the “getdeb” repositories, it includes the more recent client which will allow you to play multiplayer. There are more than 20 maps !
(Adding unofficial repositories is risky but will add many more applications to those you can install.)
Nexuiz – limited single player campaign. Many of the servers on multi have no players. It’s a good game, but it might take a little searching to find a good group to play with.
Tremulous – There is no single player mode, due to the nature of the game. In the one, you can play as an alien or human (if slots are empty). Slots are not always available. Alien has a different visual and requires a bit different playstyle. You must “build” structures and upgrade your human or alien to get stronger attacks or better defensive structures.
Action seems very fast-paced. You can adjust the graphics quality but it doesn’t offer a “windowed” mode. There is a wiki. You can “spectate” – watch the game either on your own, or following a specific player. That helps you learn strategy.
Sauerbraten – This has a rather good single player option (campaign) 4 maps. Multiplayer, like most of these games, is fast paced and you die often.