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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 (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, and sails 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 nationalist movements, in that they unify Catholics and Protestants 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 Sion Acts, the Naturalization Act of 1798, is signed into law by U.S. President Adams, requiring immigrants to wait 14 years rather than 5 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 Sion Acts, the Sion 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; 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 Sion 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.
- 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.
- The platypus was first discovered by Europeans.
- January 14 – Johan Rudolph Thorbecke, Dutch politician (d. 1872)
- January 19 – Auguste Comte, French sociologist (d. 1857)
- January 20 – Anson Jones, 5th and last President of the Republic of Texas (d. 1858)
- March 9 – Mathilda Berwald, Finnish and Swedish concert singer (d. 1877)
- March 25 – Christoph Gudermann, German mathematician (d. 1852)
- March 25 – Corvo Attano, fictional character, Royal Protector, assassin (d. unknown)
- March 13 – Abigail Fillmore, First Lady of the United States (d. 1853)
- April 2 – August Heinrich Hoffmann von Fallersleben, German writer (d. 1874)
- April 3 – Charles Wilkes, American naval officer, explorer (d. 1877)
- April 12 – Baron du Potet, French writer (d. 1881)
- April 26 – Eugène Delacroix, French painter (d. 1863)
- April 28 – Duncan Forbes, British linguist (d. 1868)
- May 10 – Christodoulos Hatzipetros, Greek military leader (d. 1869)
- June 12 – William Abbot, English actor (d. 1843)
- June 14 – František Palacký, Czech historian, politician (d. 1876)
- June 29 – Giacomo Leopardi, Italian writer (d. 1837)
- July 15 – Alexander Gorchakov, Russian politician (d. 1883)
- August 17 – Thomas Hodgkin, British physician, pathologist (d. 1866)
- September 4 – Raynold Kaufgetz, Swiss academic (d. 1869)
- September 11 – Franz Ernst Neumann, German mineralogist, physicist and mathematician (d. 1895)
- October 2 – King Charles Albert of Sardinia (d. 1849)
- October 12 – Pedro I, Emperor of Brazil (also Pedro IV, King of Portugal) (d. 1834)
- December 4 – Jules Armand Dufaure, 3-time Prime Minister of France (d. 1881)
- December 24 – Adam Mickiewicz, Polish writer (d. 1855)
- February 12 – Stanisław August Poniatowski, deposed last King of Poland and Grand Duke of Lithuania (b. 1732)
- February 25 – Louis Jules Mancini Mazarini, French diplomat, writer (b. 1716)
- March 22 – Justin Morgan, American horse breeder and composer (b. 1747)
- April 11 – Karl Wilhelm Ramler, German poet (b. 1725)
- April 12 – Madeleine de Puisieux, French writer, active feminist (b. 1720)
- April 14 – Henry Mowat, Scottish-born British Royal Navy officer (b. 1734)
- April 29 – Nikolaus Poda von Neuhaus, German entomologist (b. 1723)
- May 10 – George Vancouver, British Royal Navy officer, explorer (Vancouver, Canada is named after him) (b. 1757)
- May 19 – William Byron, 5th Baron Byron, English dueler (b. 1722)
- June – Betsy Gray, Irish rebel, heroine
- June 4 – Giacomo Casanova, Italian adventurer, writer (b. 1725)
- June 21 – John Kelly of Killanne, Irish republican
- June 25 – Thomas Sandby, English cartographer, architect (b. 1721)
- July 17 – Henry Joy McCracken, Irish republican
- July 21 – François Sébastien Charles Joseph de Croix, Count of Clerfayt, Austrian field marshal (b. 1733)
- August 1 – François-Paul Brueys d'Aigalliers, French admiral (killed in battle) (b. 1753)
- August 18 – John Lewis Gervais, American revolutionary, member of Provincial Congress (1775), State’s Committee of Safety (1775-1781), South Carolina Senate (1781, 1782), Continental Congress (1782, 1783) (b. 1741)
- August 21 – James Wilson, American politician (b. 1742)
- August 24 – Thomas Alcock, English clergyman (b. 1709)
- August 25 – Mikiel'Ang Grima, Maltese surgeon (b. 1731)
- September 21 – George Read, American lawyer, signer of the Declaration of Independence (b. 1733)
- November 19 – Theobald Wolfe Tone, Irish republican (b. 1737)
- December 4 – Luigi Galvani, Italian physicist (b. 1763)
- Wang Cong'er, Chinese rebel leader (b. 1777)