Who published the Federalist Papers defending the Constitution?

Alexander Hamilton, James Madison and John Jay published The Federalist Papers under the name of Publius. The essays originally appeared in three New York newspapers, the Independent Journal, the New York Packet, and the Daily Advertiser, in 1787 and 1788 with the intention of convincing the States to ratify the new Constitution in place of the old government organized under the Articles of Confederation.

James Madison
(28 papers: 10, 14, 37-58 and 62-63)
Alexander Hamilton (52 papers: 1, 6-9, 11-13, 15-36, 59-61, and 65-85)
John Jay wrote papers 2-5 (Foreign Affairs) and 64 (on the Senate).

All of the essays were signed Publius and the actual authors of some are in dispute, but the general consensus is that Alexander Hamilton wrote 52, James Madison wrote 28, and John Jay contributed the remaining five.

In total, the Federalist Papers consist of 85 essays outlining how this new Republican form of government would operate and why it was the best choice for the individual States and for the United States of America as a whole.

The Federalist Papers remain today as an excellent reference for anyone who wants to understand the U.S. Constitution. They should be contrasted with the contradictory essays of the Anti-Federalists, whose authorship is less clear.