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1798 (MDCCXCVIII)was a common year starting on Monday of the Gregorian calendar and a common year starting on Friday of the Julian calendar, the 1798th year of the Common Era (CE) and Anno Domini (AD) designations, the 798th year of the 2nd millennium, the 98th year of the 18th century, and the 9th year of the 1790s decade. As of the start of 1798, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 4 – Constantine Hangerli enters Bucharest, as Prince of Wallachia.
- January 22 – A coup d'état is staged in the Netherlands (Batavian Republic). Unitarian Democrat Pieter Vreede ends the power of the parliament (with a conservative-moderate majority).
- February 10 – The papacy is removed from power, by French General Louis-Alexandre Berthier.
- February 15 – U.S. Representative Roger Griswold (Fed-CT) beats Congressman Matthew Lyon (Dem-Rep-VT) with a cane after the House declines to censure Lyon earlier spitting in Griswold's face; the House declines to discipline either man.
- March 5 – French troops enter Bern.
- March 7 – French forces invade the Papal States and establish the Roman Republic.
- April 7 – The Mississippi Territory is organized by the United States, from territory ceded by Georgia and South Carolina; later it is twice expanded, to include disputed territory claimed by both the U.S. and Spain (which acquired territory in trade with Great Britain).
- April 12 – The Helvetic Republic, a French client republic, is proclaimed following the collapse of the Old Swiss Confederacy, after the French invasion.
- April 26 – France annexes Geneva.
- April 30 – The United States Department of the Navy is established as a cabinet-level department. Benjamin Stoddert, a civilian businessman, is appointed as the first Navy Secretary by President Adams.
- May 9 – Napoleon sets off for Toulon, sailing aboard Vice-Admiral Brueys's flagship L'Orient; his squadron is part of a larger fleet of over 300 vessels, carrying almost 37,000 troops.
- May 23 – Irish republicans and nationalists, known as the Society of United Irishmen, launch a rebellion against British rule, in expectation of greater support from France, which only sends 1,100 men. The United Irishmen are unique amongst Irish republican/ nationalist movements, in that they unify Catholics and Protestants (Anglican Presbyterian Methodist Baptist etc) around republican ideals. The rebellion rages sporadically, but is defeated by the British by October.
- June 12
- June 13 – Mission San Luis Rey de Francia is founded in California.
- June 18 – The first of the four Alien and Sedition Acts, the Naturalization Act of 1798, is signed into law by U.S. President Adams, requiring immigrants to wait 14 years rather than five years to become naturalized citizens of the United States. On June 25, another law is signed authorizing the imprisonment and deportation of any non-citizens deemed to be dangerous.
- July 1 – Egyptian Campaign: Napoleon disembarks his French army in Marabout Bay.
- July 7
- July 11 – The United States Marine Corps is re-established under its present name.
- July 12 – Battle of Shubra Khit: French troops defeat the Mamelukes, during Napoleon's march from Alexandria to take Cairo.
- July 14 – The fourth of the Alien and Sedition Acts, the Sedition Act of 1798 is signed into law, making it a federal crime to write, publish, or utter false or malicious statements about the United States government.
- July 16 – The Relief of Sick and Disabled Seamen Act is signed into law, creating the Marine Hospital Service, the forerunner to the current United States Public Health Service Commissioned Corps.
- July 21 – Battle of the Pyramids: Napoleon defeats Ottoman forces near the Pyramids.
- July 24 – Napoleon occupies Cairo.
- July 31 – A second round of elections are held in the Netherlands (Batavian Republic); no general elections this time.
- August 1 – Battle of the Nile (near Abu Qir): Lord Nelson defeats the French navy under Admiral Brueys. 11 of the 13 French battleships are captured or destroyed, including the flagship Orient whose magazine explodes; Nelson himself is wounded in the head.
- August 22 – French troops land at Kilcummin in County Mayo, to assist the Irish rebellion.
- September – Charles Brockden Brown publishes the first significant American novel, the Gothic fiction Wieland: or, The Transformation; an American Tale.
- September 5 – Conscription is made mandatory in France by the Jourdan Law.
- September 10 – The Piedmontese Republic is declared in the territory of Piedmont.
- September 10 – Battle of St. George's Caye: Off the coast of British Honduras (now Belize), a group of British nationals and African slaves defeat a force sent from Mexico to drive them out.
- September 18 – Lyrical Ballads is published anonymously by Samuel Taylor Coleridge and William Wordsworth, inaugurating the English Romantic movement in literature.
- October 2 – The Cherokee nation signs a treaty with the United States allowing free passage through Cherokee lands in Tennessee through the Cumberland Gap through the Appalachian Mountains from Virginia into Kentucky.
- October 7 – U.S. Representative Matthew Lyon of Vermont becomes the first member of Congress to be put on trial for violating the new Sedition Act of 1798.
- October 12
- November 4 – The Russo-Ottoman siege of Corfu begins.
- November 8 – British whaler John Fearn becomes the first European to land on Nauru.
- November 28 – Trade between the United States and modern-day Uruguay begins when John Leamy's frigate John arrives in Montevideo.
- December 5 – Peasants War in the Southern Netherlands: The revolt is crushed in Hasselt; during the uprising it is estimated that 5,000 to 10,000 people have been killed.
- December 6 – General Joubert of the Piedmontese Republic occupies the Sardinian capital of Turin.