| 1799–1825 | [maths] | The French mathematician and physicist Pierre-Simon Laplace publishes the five-volume Traité de mécanique céleste/Celestial Mechanics, which applies calculus to the motions of celestial bodies and Isaac Newton's theories of the Solar System to show how its stability is implicit in the law of gravitation. |
| 1800–1850 | USA [consumer products] | A revolution in retail and wholesale trade occurs: specialization transforms the urban retail market, replacing the general store with individual stores for hardware, groceries, dry goods, furnishing, books, tobacco, and so on. Cash-only sales policies are instituted around 1806. |
| 1810–1859 | USA [agriculture] | US cotton production, the vast majority of which is grown in the southern states, rises from 171,000 bales in 1810 to just under 5.4 million in 1859. |
| 1813 | Sweden [chemistry] | Swedish chemist Jöns Jakob Berzelius introduces the modern system of chemical symbols. |
| 1813 | England [fiction] | The English writer Jane Austen publishes her novel Pride and Prejudice. She completed it in 1797 under the title First Impressions. |
| 1813 | Germany [fiction] | The German writer Adelbert von Chamisso (Louis-Charles-Adélaïde Chamisso de Boncourt) publishes his tale Peter Schlemihls wundersame Geschichte/Peter Schlemihl's Remarkable Story. |
| 1813 | Wales [literature and language] | The Welsh social reformer Robert Owen publishes A New View of Society. |
| 1813 | Austria [music] | Austrian composer Franz Schubert completes his Symphony No 1 in D (D 82) and his String Quartets No 3 (D 36), No 4 (D 46), No 5 (D 68), and No 6 (D 74). |
| 28 February 1813 | Prussia, Russian Empire [treaties] | Prussia agrees, by the Alliance of Kalisz with Russia, to conduct a joint campaign in Saxony and Silesia against the French emperor Napoleon I and the Confederation of the Rhine (association of German states under French protection). Prussia is to regain all territory lost since 1806. An invitation to join the war is extended to Britain and Austria, and the agreement becomes the genesis of the Fourth Coalition against France. |
| 19 March 1813 | Scotland, Africa [births and deaths] | David Livingstone, Scottish missionary and explorer who explores much of East Africa in search of the source of the Nile, born in Blantyre, Lancashire, Scotland (–1873). |
| 22 May 1813 | Germany [births and deaths] | (Wilhelm) Richard Wagner, German dramatic composer and theorist who writes the operatic sequence Der Ring des Nibelungen/The Ring of the Nibelung, born in Leipzig, Germany (–1883). |
| 21 June 1813 | UK, France, Spain [Napoleonic Wars (1803–15)] | British forces under the Duke of Wellington (Arthur Wellesley) completely rout the French army of Marshal Jean-Baptiste Jourdain at Vittoria in northern Spain, forcing Joseph Bonaparte to flee back to France. |
| 10 October 1813 | Parma [births and deaths] | Giuseppe Fortunino Francesco Verdi, Italian operatic composer, born in Le Roncole, near Busseto, Duchy of Parma (–1901). |
| 12 October 1813 | Persia, Russian Empire [treaties] | By the peace of the Treaty of Gulistan, Persia cedes the Caucasus region to Russia, continuing the extension of Russian influence southwards. |
| 16 October - 19 October 1813 | France, Prussia, Austrian Empire, Russian Empire, Saxony, Confederation of the Rhine, Westphalia [Napoleonic Wars (1803–15)] | Opposed by the Prussian army in the northwest and Austro-Russian forces in the south, the French army under the emperor Napoleon I is heavily defeated in the ‘Battle of the Nations’ at Leipzig in Saxony, and retreats. Allied victory leads to the dissolution of the Confederation of the Rhine (the association of German states under French protection) and of the kingdom of Westphalia. |
| 6 November 1813 | Mexico, Spain [decolonization] | Mexico declares itself independent of Spain. |
