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.
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.
