All the public transport in Oslo and the surrounding county Akershus is part of the same ticket and price system, operated by Ruter. Ruter's tickets are valid for buses, trams, subways, ferries (not the Bygdøy ferry) and local trains.
Free travel with the Oslo Pass
Public transport within zone 1 (Oslo) and zone 2 is free with the Oslo Pass. This also includes the ferry to the Bygdøy museums, which is not included in the regular tickets.
Read more: Free public transport with the Oslo Pass