What are the state courts in descending order?

The main federal courts are the Supreme Court of the United States, the 13 Federal Circuit Courts of Appeals, and the United States District Courts, which are the federal trial courts. There are other smaller specialty courts, such as the Court of International Trade located in New York City which could be said to sit on a level equal with that of the Federal District Courts. There are also numerous specialized Administrative Courts which handle a variety of matters falling within the scope of federal jurisdiction. These Administrative Courts, however, are part of the Executive Branch of the US Government, not the Judicial Branch. These are thus not so-called Article III courts, meaning they were not established under Article III of the U.S. Constitution (the Article setting forth the existence of the Supreme Court), and judges on these courts serve at the pleasure of the President rather than for life.