There were three authors of the Federalist Papers.
James Madison (28 papers: 10, 14, 37-58 and 62-63) and Alexander Hamilton (52 papers: 1, 6-9, 11-13, 15-36, 59-61, and 65-85) wrote most of the Federalist Papers, but 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 under 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 government would operate and why this type of government was the best choice for the United States of America.
The Federalist Papers remain today as an excellent reference for anyone who wants to understand the U.S. Constitution.