Apps Login System using Gmail

I'm looking to create an application for my university which will allow users to comment and check-in to places, similar enough to how Foursquare operates.

I've just one question, when creating a login system, would it be possible to just have users login just by using their gmail account? So instead of making a server which has all these users registering to the server, could they instead just simply login with their gmail account, removing the need to register with the application at all?