Can you buy a computer game and play it without having the internet

yes.


There are many games including much older titles that were released without a multiplayer option so there is no need of an Internet connection to play.

There are titles in which having an Internet connection allows the player to play on-line with others but is not required because it also can be played as a single player campaign or single player mode.

Finally there are some titles such as World of Warcraft that require the the player to have an Internet connection in order to participate in the game play.

Details of what is required to use the game should be printed on the game box.