The ordinary courts of Norway are of general jurisdiction, adjudicating both civil and criminal cases. You can read more about the history and independence of the courts here.
The Norwegian justice system is hierarchical and has three main levels: the first instance – District Courts (tingrettene), the second instance – the Courts of Appeal (lagmannsrettene) and the third instance – Supreme Court (Høyesterett). In addition, the Appeals Committee of the Supreme Court, composed of three Supreme Court judges in each case, makes decisions in certain interlocutory cases and determines whether the Supreme Court will hear a case. You can read more about the structure of Norwegian courts here.
There are 23 District Courts and 6 Courts of Appeal.
The Land Consolidation Courts of Norway (jordskiftedomstolene) hear cases regarding property rights. Decisions from the Land Consolidation Courts can be appealed to the ordinary Courts of Appeal.
The Labour Court of Norway (Arbeidsretten) is a limited jurisdiction court located in Oslo that hears disputes regarding collective labour agreements. Decisions from the Labour Court of Norway are final and cannot, as a general rule, be challenged through an appeal.
The Finnmark Land Tribunal (Utmarksdomstolen for Finnmark) was established in 2014 to consider disputes concerning the rights to land and water in the Finnmark Region of Norway which the Sami people and others have acquired through their use over a long period of time. Decisions from The Finnmark Land Tribunal may be appealed directly to the Supreme Court.
The National Insurance Court (Trygderetten) is an independent national appellate body that considers disputes over social security and pension. Decisions from the National Insurance Court can be appealed directly to a Court of Appeal (lagmannsrett), thus bypassing a decision in a district court (tingrett).