What is the basic logic or structure of the U.S. court system?

The United Court system was established based on Article III of the Constitution and although is present in every state is structures independently from state courts. A pyramid with 3 levels can logically represent the structure of the U.S. Court system.
The bottom of the pyramid is made of of 94 District Courts. Every state has at least one United States District Court; however, these courts only have jurisdiction over cases in which the U.S. is a party in the lawsuit or a federal or constitution law has been violated, not cases involving state matters.These courts hear both civil and criminal cases according to individuals' constitutional rights to representation, a trial by jury, and a speedy trial.
The middle of the pyramid consists of 13 Circuit of Appeals Courts. These Courts are responsible for hearing cases that have already been heard by a lower court in which a plaintiff has submitted an appeal for a variety of reasons such as inadequate counsel. The Judged of this court are burdened with deciding whether the law was applied correctly by the previous court. From here cases may be appealed again to the Supreme Court, be resolved, or be sent back to the lower courts to be heard again.
The top of the pyramid is the United States Supreme Court. The Supreme Court is the last to rule on a case that has been appealed. Not all cases submitted to this court are herd; however, the ones that are typically involve instances in which the constitution has been violated. The nine justices of the Supreme Court of burdened with interpreting the constitution and their decisions set powerful legal precedence.

The federal court system has three components with three different levels of power: The U.S. Supreme Court, the U.S. District Court, and the U.S. Circuit Court of Appeals. Article III of the Constitution created The Supreme Court, which is the highest court in the system, and Article III also created a system of lower courts, which includes 13 U.S. circuit courts of appeals (or appellate courts) and 94 U.S. district courts (or trial courts).
U.S. district courts exist in every state and contain panels of two to eight judges. Each case is tried by a judge and decided on by a jury. These district courts, or trial courts, rule in civil suits that involve a violation of a person’s constitutional rights or a violation of U.S. laws. They also rule in civil or criminal cases in which the United States is a party in the lawsuit. The U.S. district courts have no power to hear appeals from lower courts. Appeals are handled by the U.S. circuit courts of appeals, or appellate courts.
These 13 U.S. circuit courts of appeals rule in both civil and criminal cases in which one or both parties are contesting the judgment in a U.S. district court. The job of the appellate courts is to determine whether the law was correctly applied in the original judgment. Thus, they have a lot of power in the U.S. court system and often set legal precedents. Each case tried in an appellate court is heard by three judges.