If memory serves you have:
Campaign - The single player story mode.
Arcade - You can create a custom team battle (team deathmatch) or onslaught (you alone vs ai), there are also preset games based on these two modes.
There is also training but it's very basic.
There's a single player campaign mode and an "Arcade" mode in which you can take part in battles again AI enemies on your own, or with a 2nd player in split-screen (either co-op or versus).
The single player campaign is basically just a bunch of offline bot matches, with some cut scenes in between... so don't get your hopes too high. It's certainly nothing like the kind of single player campaign you got in Battlefield 4.
So far, you can't access space battles in offline mode... or at least, I haven't been able to find any without going into online multiplayer mode.
