The Federalist Papers (originally published as just The Federalist) are a collection of essays published in newspapers in 1787-1788 arguing for the ratification of the American Constitution. Each was published under the pseudonym "Publius" though most were written by Alexander Hamilton and James Madison. (There are a few written by John Jay.) They were collected and published in groups during the ratification of the Constitution and then published as a group following ratification. They are among the most important documents articulating the political philosophy underlying the American Constitution itself.
The essays are widely available in many forms and have been published by many presses. You can get a free version from Project Gutenburg. The Wikipedia entry for the Federalist Papers contains extensive links and structure to the papers and cross-references to each of the essays.
We will be discussing selections focused on the arguments for the basic structure of the proposed government -- the separation of powers, the importance of commerce, the primacy of union, and the problem of faction:
1 - Outline of the essay series
10 - Defense of large republics/addressing the problem of faction
11, 12 - importance of trade and commerce to the new republic
14 - Defense of the extended republic; that the proposed republic is a new, modern government
15-17 - Why more federal power is necessary and too much state power is problematic
39 - On republican principles of government
47-51 - On the separation of powers as a central, necessary feature of the proposed Constitution
I would highly recommend the Cambridge edition which contains all the essays themselves, some useful introductory material, the Articles of Confederation and the original Constitution, and the complete set of the "Letters of Brutus."