Congress has granted to the federal courts subject matter jurisdiction over the following types of cases:
1. Claims involving federal law.
2. Cases in which the federal government is a party. This includes cases against a federal employee acting in his official capacity, which is typically how the US government gets sued. Cases with "United States" in the name are generally federal criminal cases.
3. Cases between citizens of different states (diversity jurisdiction).
4. Cases between two states. Congress granted the courts jurisdiction over cases between a state and a citizen of another state, but Amendment XI gutted that.