Given the breadth of the 85 essays that composes this topic, I chose to simply provide web sites that discuss these important documents. Briefly, they were written in 1787-1788, and were used to promote the ratification of the Constitution, which appears to have been thoroughly considered, and hotly argued. The importance of these documents cannot be denied, and the fact that so many Americans aren't even aware of them, much less their purpose, is appalling (yet not surprising given today's political climate).
On Wiki-pedia - provides a history of the essays, and identifies their authors.
At the Library of Congress - provides the text of the essays.