With the League API, you can obtain the league related information, like the league name, the number of teams, the draft status, etc.
Leagues only exist in the context of a particular Game, although you can request a League Resource as the base of your URI by using the global league_key.
Users can only retrieve data for private leagues of which they are a member if they have provided a valid OAuthToken upon authenticating your application. Leagues that have been designated as public can be queried without user authentication.