<P> A term of the Supreme Court commences on the first Monday of each October, and continues until June or early July of the following year . Each term consists of alternating periods of approximately two weeks known as "sittings" and "recesses ." Justices hear cases and deliver rulings during sittings; they discuss cases and write opinions during recesses . </P> <P> In nearly all of the cases heard by the Supreme Court, the Court exercises the appellate jurisdiction granted it by Article III of the Constitution . This authority permits the Court to review--and affirm or overturn--decisions made by lower courts and tribunals . Procedures for bringing cases before the Supreme Court have changed significantly over time . Today, cases are brought before the Supreme Court by one of several methods, of which the first two account for the overwhelming majority of cases decided: </P> <Ul> <Li> By petition for a writ of certiorari, filed by a party to a case that has been decided by one of the United States courts of appeals or by the United States Court of Appeals for the Armed Forces . </Li> <Li> By petition for writ of certiorari with respect to a decision of one of the territorial or state courts, after all state appeals have been exhausted, where an issue of federal constitutional or statutory law is in question . The writ is usually issued to a state supreme court (including high courts of the District of Columbia, Puerto Rico, the U.S. Virgin Islands, Guam, the Northern Mariana Islands, and American Samoa), but is occasionally issued to a state's intermediate appellate court for cases where the state supreme court denied certiorari or review and thereby refused to hear the appeal . </Li> <Li> By petition for certiorari before judgment, which permits the Court to expedite a case pending before a United States court of appeals by accepting the case for review before the appellate court has decided it . However, Supreme Court Rule 11 provides that a case may be taken by the Court before judgment in a lower court "only upon a showing that the case is of such imperative public importance as to justify deviation from normal appellate practice and to require immediate determination in this Court ." </Li> <Li> By appeal from certain decisions of United States district courts in certain cases involving redistricting of congressional or state legislative districts, or when specifically authorized in a particular statute . </Li> <Li> By a certified question or proposition of law from one of the United States Courts of Appeals, meaning that the Court of Appeals requests the Supreme Court to instruct it on how to decide the case . This procedure was once common but is now rarely invoked; the last certificate accepted for review was in 1981 . </Li> <Li> By petition for an "extraordinary writ" such as mandamus, prohibition, or habeas corpus . These writs are rarely granted by the Supreme Court though they are more frequently granted by lower courts . </Li> </Ul> <Li> By petition for a writ of certiorari, filed by a party to a case that has been decided by one of the United States courts of appeals or by the United States Court of Appeals for the Armed Forces . </Li>

Explain the process used in deciding which cases will be heard by the supreme court