During the administrations of Washington, Adams, Jefferson and Madison, Europe was nearly constantly at war and it grew increasingly difficult for the new United States to stay out of it. Explain the situation, its problems, and the ways these early presidents sought to stay out of war, why they ultimately failed, and what the result was.

The office of the Presidency was created by the U.S. Constitution, but many of the powers of the office were still undefined by the document. The early U.S. presidents were in the unique position of determining the scope of their powers and establishing new norms, particularly in the case of foreign conflict.
George Washington, the first U.S. President, made extensive efforts to focus on domestic issues before becoming involved in foreign disputes. However, the French Revolution, was expanding into the rest of Europe, opening the door to an international crisis. After France declared war on Britain in 1793, the British became concerned about the United States' allegiances. America's longtime alliance with France might encourage the United States to break their neutrality in favor of France.
So, in 1794, the British Royal Navy seized American ships in the West Indies. It seemed like war was inevitable and many U.S. politicians, including Thomas Jefferson, thought it was the only way forward. Washington, however, felt neutrality was essential to the longevity of the early American nation. In November 1794 Washington sent John Jay, the Chief Justice of the Supreme Court, to Britain with the Jay Treaty. Its primary tenets were that Britain would compensate the United States for its interference in West Indies and provide favored nation status to American traders in exchange for Americans, offering Britain some trade advantages in the United States and paying off some Revolutionary War debts.
Ultimately, the treaty was approved by Congress on August 14, 1795, after significant debate. It was the first time the new American government had needed to arbitrate an international treaty, and it proved that the new American political system worked: big international relations decisions could be made through a process of debate and arbitration. It also reinforced Washington's belief that the United States needed to maintain neutrality and peace in order to protect her fledgling democracy--a point Washington reiterated in his Farewell Address.
John Adams, the second U.S. President, had to face the fallout from the Jay Treaty, which had angered the French. They felt betrayed by the Americans, who had previously sided with them against the British. In March 1797, John Adams sent three of his best diplomats—Charles Pinckney, John Marshall, and Elbridge Gerry—to France to meet with the foreign minister Charles de Talleyrand. The minister refused to meet with them unless they'd pay a sizable bribe andprovide a loan. The Americans refused.
When Adams received word of the French demands, he took immediate action. He took the memos from his diplomats and replaced the names of the French actors with the letters X, Y, and Z, leading the action to be called the XYZ Affair. Adams then sent the memos to Congress, which subsequently pushed through a series of defensive measures, including expanding the Department of War and creating a new executive department for the Navy. In July 1798, Congress even authorized the attack of French vessels in the Atlantic in a "quasi-war," stockpiling warships, weapons, and money in case of war--which, still, was avoided.
Thomas Jefferson, the third U.S. President, inherited this system of American neutrality (and its newly built arsenal and Department of War) which would become harder to preserve as things escalated in Europe. British soldiers began to desert in record numbers, often hiding on American ships and enlisting as merchant marines. The problem of deserting British sailors became so extreme that British "press gangs" were dispatched to board American ships and take anyone off who appeared to be British. Unfortunately, these gangs often removed Americans alongside the British soldiers. The conflict came to a head in 1807, when the British ship H.M.S Leopard opened fire on the American ship U.S.S. Chesapeake after the Chesapeake refused to allow British press gangs aboard. Three American sailors were killed, and the ship was raided.
Jefferson was in a tight spot: he feared any move he made would lead to war. His solution, then, was to ban trade with Europe altogether. This was called the Embargo Act, and it passed through Congress in late 1807. Unfortunately, the Act only served half (or less) of its purpose. It prevented war between Britain and the United States, but it backfired economically for the Americans. After a long debate on how to proceed, Congress decided to substitute the Embargo Act with a Non-Intercourse Act in March 1809, which removed every nation but France and Britain from the embargo. Three days before leaving office, the now highly unpopular President Jefferson signed it into law. Peace was preserved, but at a high economic cost.
James Madison was the fourth U.S. President. In 1810, Madison attempted to rectify the economic disaster caused by the Embargo and Non-Intercourse Acts by passing a bill known as Macon's Bill Number 2. Under this legislation, trade remained free between Britain, France, and the United States, but if either Britain or France violated the United States' neutrality, the United States would immediately ban the nation from trade.
This Bill failed to end ongoing British impressment and French attacks on American ships. Even so, Madison remained firm in his desire to prevent war. His new Congress, however, was less interested in doing so. In 1811, Congress met and elected Henry Clay, an outspoken and colorful Kentuckian, to be Speaker of the House. Clay led a group of Congressmen from the Northwest and Southwest territories known as "War Hawks." They feared the British were allying themselves with the American Indians, and believed the only way forward was to defeat the British and the American Indians on American soil. They wanted a war.
Despite his reticence, Madison officially declared war on June 18, 1812. As it turned out, Madison was right to be skeptical. The Americans were completely unprepared for war. The U.S. Army was incredibly small at this time, with less than 12,000 men enlisted when the war broke out. State militias, which weren't under federal government control, frequently refused to carry out military orders since they disagreed with the war on principle. The war was also expensive and difficult to finance.
Ultimately, the War of 1812 left Britain and the United States exactly as they had been before: both living on the American continent, with the United States' neutrality intact. The war had nearly bankrupted the United States, and had also divided the Northeastern states, who were anti-war, from the inland states, who had pushed for it.
Americans were realizing that George Washington's policy of neutrality seemed to have been the right move. The War of 1812 had failed to change anything except the nation's finances, so Madison and his Congress quickly reverted to a focus on peace. For a while, it worked: this was known as the Era of Good Feelings. James Monroe, the fifth President, would inherit a seemingly stable nation. Unfortunately, as the United States' short history had already demonstrated, war was always on the horizon--and the President was not always able to prevent it.