United States Supreme Court
Hears cases (of its choice) from federal and state courts.
Federal circuit courts of Appeals
The federal system has one level of appeal before the Supreme Court. These are "Circuit Courts of Appeals." There are 13 of them.
state highest court (usually the state supreme court)
The states set up their court systems differently, but they all have a highest court. Cases judged in the highest state court may appeal to the United States Supreme Court.
federal district courts
The first level court in the federal system is a federal "District Court." There are 94 of them.
State appellate courts
This is an appeals court from the state trial court. 39 out of 50 states have them.
State Trial Courts
All 50 states have trial courts, the first level court of the state system.