The U.S. President's role to make treaties resides in Article 2, Section 2 of the U.S. Constitution. However, that role is with the "advice and consent" from the U.S. Senate provided two-thirds of the Senators present concur."
A good historical overview about the "advice and consent" from the U.S. Senate is available on the Senate's history site discussing Treaties.
Treaties in Force: annually published by the U.S. Department of State and covers bilateral treaties, multilateral treaties, and international agreements. It is organized in two sections (bilateral & international agreements is section 1 and multilateral & international agreements is section 2) and then alphabetically by country recognized by the United States and then by broad topical area. Citations are provided. Arrangement for territorial possessions are listed at the end of that country.
Treaties and Other International Acts Series (TIAS) has been the official publication format for treaties and agreements that have entered into force for U.S since 1945. This publication is no longer issued in print but you will see TIAS information in treaty citations.
United States Treaties and Other International Agreements (UST) was a bound compilation from 1950-1982 of TIAS prints. This publication is no longer issued in print.
United States Treaty Series (TS) covers advice-and-consent treaties.It is a precursor to the TIAS series covering 1795-1945 and was printed by the Department of State.
Executive Agreement Series (EAS) was created to include the growing body of executive agreements in the post WWI period (1928-1945).. Earlier executive agreements can be found in the Treaty Series
U.S. Statutes at Large (Stat.) Bound volumes containing advice-and-consent treaties until 1948.
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