This is admittedly an educated guess and may be applicable only in the US: But I believe the answer would be Municipal Courts or County-level court systems probably hear the most cases due simply to the sheer number of misdemeanor and traffic cases that are heard each day.
It can depend on what kind and type of cases you are referring to. Probably the most overwhelmingly busy of all of the courts is Traffic Court. Other than that, county level and state circuit courts are probably the most busy level of the court system.
Trial courts, known as Federal District Court.
state courts
federal court
The Supreme Court is brought a large number of cases every year to review, but they do not have to hear all of them. They choose from cases that have already gone through state or federal courts where one of the parties was unhappy with the previous decision.
The Supreme Court of the United States was created in 1789. Most of the cases the court hears come from lower courts. Each year, the Supreme Court receives 7,000 or more requests to hear cases from lower courts.
evaluate the decisions of lower federal court
US Court of Federal Claims would hear those cases.
US District Courts have original (trial) jurisdiction over the majority of cases heard in the federal court system.US Special Courts, such as US Tax Court, US Bankruptcy Court, and the US Court of Federal Claims, also hear a large number of cases.
the Federal Court.
Generally, federal criminal cases are tried in US District Court.
Most federal criminal cases are tried in US District Court.
In most cases I have read the civil cases heard at the Federal level are cases that directly question someone's rights and apply to a large number of people. The cases heard at a local level can also be promoted to Federal cases. For example if you have a property dispute with your neighbor it will not go to federal court; however, if you have a court that disputes whether its legal for you to carry a concealed weapon or practice free speech you could proceed to the Federal Court.
Yes, it is a federal court.
Federal trial courts almost always have original jurisdiction in the federal system.
Bankruptcy Court is filed in Federal District Court, however, exemptions claimed are state regulated.
Federal tax cases
how the powers of the Supreme Court and federal law were extended by landmark court cases
US district courts have trial jurisdiction (aka original jurisdiction) over federal court cases.
The US District Court