1796

January–March

• January 16 – The first Dutch elections are held for the National Assembly of the Batavian Republic.
• February 1 – The capital of Upper Canada is moved from Newark to York.
• February 9 – The Qianlong Emperor of China abdicates at age 84 to make way for his son, the Jiaqing Emperor.
• February 15 – French Revolutionary Wars: The Invasion of Ceylon ends when Johan van Angelbeek, the Batavian governor of Ceylon, surrenders Colombo peacefully to British forces.
• February 16 – The Kingdom of Great Britain is granted control of Ceylon by the Dutch.
• February 29 – Ratifications of the Jay Treaty between Great Britain and the United States are officially exchanged, bringing it into effect.
• March 9 – Widow Joséphine de Beauharnais marries General Napoléon Bonaparte.
• March 20 – The U.S. House of Representatives demands that the U.S. State Department supply it with documents relating to the negotiation of the Jay Treaty; President Washington declines the request, citing that only the U.S. Senate has jurisdiction over treaties.
• March 26 – Napoleon Bonaparte arrives at Nice to take command of the Army of Italy, which is scattered in detachments as far as Genoa.
• March 30 – Carl Gauss obtains conditions for the constructibility by ruler and compass of regular polygons, and is able to announce that the regular 17-gon is constructible by ruler and compasses.

  April–June

• April 2 – The only night of the supposed Shakespearean play Vortigern and Rowena ends in the audience's laughter.
• April 12 – War of the First Coalition – Battle of Montenotte: Napoleon Bonaparte gains his first victory as an army commander.
• April 21 - War of the First Coalition - Battle of Mondovi: Napoleon Bonaparte decisively defeats the army of Piedmont Sardinia, leaving its capital of Turin defenseless. This convinces Piedmont to sign an armistice and withdraw from the war, turning the war in Italy decisively in France's favor.
• April 26 – The French proclaim the Republic of Alba on the occupied territories. Two days later, King Victor Amadeus III of Sardinia signs the Armistice of Cherasco, in the headquarters of Napoleon. The fortresses of Coni, Tortoni and Alessandria, with all their guns, are given up.
• April 27 – Case of the Lyons Mail: During the night, five highwaymen attack the mail between Paris and Lyon, kill the postmen and steal the funds sent to the armies in Italy.
• April 28 – In an impassioned speech, U.S. Representative Fisher Ames of Massachusetts persuades his fellow members of the House to support the Jay Treaty.
• May 6 – Napoleon Bonaparte forms an advanced guard under General Claude Dallemagne. He sends this force along the south bank of the Po River, to cross it with boats at Piacenza.
• May 10
• * War of the First Coalition – Battle of Lodi: General Napoleon Bonaparte defeats the Austrian rearguard, in forcing a crossing of the bridge over the Adda River in Italy. The Austrians lose some 2,000 men, 14 guns, and 30 ammunition wagons.
• * Persian Expedition of 1796: Russian troops storm Derbent.
• May 14 – Edward Jenner administers the first smallpox vaccination, in England.
• May 15 – Napoleon's troops take Milan.
• May 20 – The last mock Garrat Elections are held in Surrey, England.
• June 1
• * The French-Republican army divisions of the Army of Italy invade the territories of Venice.
• * Tennessee is admitted as the 16th U.S. state.
• June 4 - The Siege of Mantua begins when Napoleon lays siege to the city of Mantua, Austria's final stronghold in Northern Italy. The siege, and Austria's attempts to relieve it, will take the majority of the Italian campaign.
• June 6–7 – Ragunda lake in Sweden bursts and drains completely leaving the Döda fallet dry.
• June 21 – Scottish explorer Mungo Park becomes the first European to reach the Niger River.
• June 23 – Napoleon Bonaparte seizes the Papal States, which become part of the revolutionary Cisalpine Republic. Pope Pius VI signs the Armistice of Bologna, and is forced to pay a contribution.

  July–September

• July 10 – Carl Friedrich Gauss discovers that every positive integer is representable as a sum of at most 3 triangular numbers.
• July 11 – The United States takes possession of Detroit from Great Britain, under the terms of the Jay Treaty.
• July 21 – Mungo Park reaches Ségou, the capital of the Bamana Empire.
• July 22 – Surveyors of the Connecticut Land Company name an area in Ohio Cleveland, after Gen. Moses Cleaveland, the superintendent of the surveying party.
• July 29 – The Habsburg army under Marshal Wurmser advances from the Alps, and captures Rivoli and Verona. The French abandon the east bank of the Mincio River, the outnumbered division of Masséna retreats towards Lake Garda.
• August 4 – French Revolutionary Wars: Battle of Lonato – The French Army of Italy under Napoleon crushes an Austrian brigade.
• August 5 – French Revolutionary Wars: Battle of Castiglione – The French Army of Italy under Napoleon defeats the Habsburg army under Marshal Wurmser, who thus fails to break the Siege of Mantua, and is forced to retreat north up the Adige Valley.
• August 9 – The Wearmouth Bridge in England, designed by Rowland Burdon in cast iron, opens to traffic. Its span of makes it the world's longest single-span vehicular bridge extant at this date.
• August 10 – A mob of peasants overtakes the Convent of St. Peter and murders Ignaz Anton von Indermauer.
• August 19 – Second Treaty of San Ildefonso: Spain and France form an alliance against Great Britain.
• September 2 – Jewish emancipation in the Batavian Republic.
• September 8 – French Revolutionary Wars: Battle of Bassano – French forces under Napoleon Bonaparte and André Masséna defeat the Austrians in Veneto. Wurmser retreats towards Vicenza with just 3,500 men of his original 11,000 left to him.
• September 9 – French Revolutionary Wars: Action of 9 September 1796 – A naval engagement between French and British squadrons off Sumatra ends inconclusively.
• September 9 – Grenelle camp affair, a failed uprising by supporters of Gracchus Babeuf against the French Directory
• September 15 – Siege of Mantua: Napoleon Bonaparte fights a pitched battle at La Favorita on the east side of the Mincio River. The Austrians withdraw into the fortress of Mantua, which is crowded with nearly 30,000 men. Within six weeks, 4,000 die from wounds or sickness.
• September 17 – U.S. President George Washington issues his Farewell Address, which warns against partisan politics and foreign entanglements. In addition, he sets a precedent by declining to run for a third term.
• September 28 – Empress Catherine the Great signs an agreement with Great Britain, formally joining Russia to the coalition.

  October–December

• October 19 – French Revolutionary Wars: Battle of Emmendingen – Austrian forces force the French to retreat, but commanding generals on both sides are killed.
• October – Jane Austen begins writing her first draft of Pride and Prejudice, under the title First Impressions.
• November 3 – John Adams defeats Thomas Jefferson, in the 1796 U.S. presidential election.
• November 4 – The Treaty of Tripoli is signed at Tripoli.
• November 6
• * Catherine the Great dies, and is succeeded by her son Paul I of Russia. His wife Sophie Marie Dorothea of Württemberg becomes Empress consort.
• * French forces under Masséna attack the Austrian army at Fontaniva. After a desperate assault he is outnumbered, and forced to retreat to Verona.
• November 12
• * Battle of Caldiero: French forces are defeated by the Austrians at Caldiero, and pushed back to Verona. This marks Napoleon's first defeat, losing nearly 2,000 men and 2 guns.
• * Groton, New Hampshire is incorporated as a town.
• November 17 – Battle of Arcole: French forces under General Napoleon defeat the Austrians at Arcole. After a bold maneuver, he outflanks the Austrian army under Freiherr József Alvinczi, and cuts off its line of retreat. Alvinczi is forced to take up a defensive position behind the Brenta River.
• December – The British government begins work on a 40-acre site at Norman Cross, for the world's first purpose-built prisoner-of-war camp.
• December 7 – The U.S. Electoral College meets to elect John Adams president of the United States.
• December 18 – British Royal Navy ship HMS Courageux is wrecked on the Barbary Coast with the loss of 464 of the 593 onboard.

  Date unknown

• The Spanish government lifts the restrictions against neutrals trading with the colonies, thus acknowledging Spain's inability to supply the colonies with needed goods and markets.
• Robert Burns's version of the Scots poem Auld Lang Syne is first published, in this year's volume of The Scots Musical Museum.
• Annual British iron production reaches 125,000 tons.
• Rizla rolling papers established.