U.S. relations with many countries are governed by a number of treaties, both multilateral and bilateral. Some of the more important multi-lateral treaties are:
Digest of International Law
Hague Convention on Legalization of Foreign Public Documents
Vienna Convention on Consular Relations
Hague Evidence Convention
Hague Conference on Private International Law
Hague Service Convention
Hague Child Abduction Convention
Hague Adoption Convention
Treaties in Force
Council of Europe Treaty Office
Organization of American States (OAS) Treaties Page
United Nations Treaties Page
The U.S. has bilateral treaties with a number of countries concerning consular matters. You can read about these here: Bilateral Consular Conventions