Yes, you can play both the campaign mode and multiplayer mode in Call of Duty: Modern Warfare 3 offline. The campaign mode can be played in its entirety in offline mode, and a Private Multiplayer mode allows you to access all of the maps and modes present in Multiplayer.

You can play the game offline, but there are several things you need to do first: Install MW3 via disc or download. If you're using a disc, you'll be prompted to download a 70+GB patch. If you purchased a digital download, skip to the next step.