WASHINGTON — After back-to-back terms ending in historic rulings that riveted the nation, the Supreme Court might have been expected to return to its usual diet of routine cases that rarely engage the public.

Instead, the court’s new term, which starts Monday, will feature an extraordinary series of cases on consequential constitutional issues, including campaign contributions, abortion rights, affirmative action, public prayer and presidential power.

“This term is deeper in important cases than either of the prior two terms,” said Irving L. Gornstein, the executive director of the Supreme Court Institute at Georgetown University.

An unusually large number of the new cases put important precedents at risk, many in areas of the law the court has been rapidly revising since the retirement of Justice Sandra Day O’Connor. She was at the court’s ideological center, and her moderate instincts played a crucial role in shaping the court’s jurisprudence on abortion, race, religion and the role of money in politics.