Before there was a U.S. Navy, before there was a United States, there was the Continental Navy (additional information here). What initially passed for a navy then were thirteen lightly armed frigates, along with various other classes of ships. They were outclassed by their British counterparts, and none of them survived beyond 1781 having been captured or destroyed, some of them by American hands. The story of the beginning of the Continental Navy, the role John Adams played in its development, the naval conflicts that took place in upstate New York, the appearance of John Paul Jones, the role of France, Spain, and Holland, all of these events are chronicled in the Naval Documents of the American Revolution. This massive collection of primary sources in twelve volumes totaling over 10,000 pages covers the years 1774-1778. It is the product of the efforts of hundreds of scholars from dozens of repositories both here and abroad. Each volume is divided into the American theater and the European theater and is accompanied by numerous contemporary illustrations, extensive bibliographies, informative appendices, and a detailed index. Volume 1 appeared in 1964 with a foreword by President Kennedy, and volume 12 made its appearance in 2013; it is an ongoing project.
Additional primary sources can be consulted: The correspondence of Esek Hopkins, commander-in-chief of the United States navy; Letters and papers relating to the cruises of Gustavus Conyngham, a captain of the continental navy, 1777-1779; The journal of Gideon Olmstead: adventures of a sea captain during the American Revolution; Out-letters of the Continental Marine Committee and Board of Admiralty, August, 1776-September, 1780; Papers of William Vernon and the Navy Board, 1776-1794; The despatches of Molyneux Shuldham, vice-admiral of the Blue and commander-in-chief of His Britannic Majesty’s ships in North America, January-July, 1776; Letter-books and order-book of George, lord Rodney, admiral of the White squadron, 1780-1782; A detail of some particular services performed in America, during the years 1776, 1777, 1778, and 1779. Compiled from journals and original papers [British]; Connecticut’s Naval office at New London during the war of the American revolution, including the mercantile letter book of Nathaniel Shaw, jr.,; Life of Rear-Admiral John Paul Jones compiled from his original journals and correspondence: including an account of his services in the American Revolution and in the war between the Russians and Turks in the Black sea [autobiography]; The life and letters of John Paul Jones; Paul Jones : his exploits in English seas during 1778-1780, contemporary accounts collected from English newspapers, with a complete bibliography; The log of the Bon Homme Richard; Diary of Ezra Green, M. D., surgeon on board the continental ship-of-war “Ranger,” under John Paul Jones, from November 1, 1777, to September 27, 1778 ; Journal of the Commissioners of the navy of South Carolina October 9, 1776-March 1, 1779, July 22, 1779-March 23, 1780; Memoirs of Andrew Sherburne: a pensioner of the navy of the revolution ; and The Operations of the French fleet under the Count de Grasse in 1781-2, as described in two contemporaneous journals .
Some good secondary sources: Naval records of the American Revolution, 1775-1788. Prepared from the originals in the Library of Congress [A calendar]; The war at sea : France and the American Revolution : a bibliography; Biographical sketches of distinguished American naval heroes in the war of the revolution, between the American Republic and the Kingdom of Great Britain; Sea raiders of the American Revolution : the Continental Navy in European waters; and United States Naval History: A Bibliography. And we should not forget Mahan’s 1913 work The Major Operations of the Navies in the War of American Independence.