| 1845–1958 | Germany [earth sciences] | German naturalist and explorer Alexander von Humboldt lays the basis of modern geography with the publication of Kosmos/Cosmos, in which he arranges geographic knowledge in a systematic fashion. |
| 1871 | Egypt [opera] | The opera Aïda by the Italian composer Giuseppe Fortunino Francesco Verdi is first performed, in Cairo, Egypt (to celebrate the opening of the Suez Canal). |
| 1871 | USA [painting] | The US artist Thomas Eakins paints Max Schmitt in a Single Scull. |
| 1871 | UK [photography] | English doctor Richard Leach Maddox and English chemist Joseph Wilson Swan replace the collodion wet-emulsion photographic plate with a dry, silver-bromide sensitized, gelatin-emulsion plate. The gelatin emulsions go on sale in 1873 and the plates in 1876. They revolutionize photography. |
| 1871 | USA [political theory] | The US poet Walt Whitman publishes his political tract Democratic Vistas, arguing that democracy and individualism are compatible. |
| 1871 | England [fiction] | The English writer and mathematician Lewis Carroll writes the children's classic Through the Looking Glass and What Alice Found There. |
| 1871 | England [fiction] | The English writer George Eliot (pseudonym of Mary Anne Evans) publishes the first part of her novel Middlemarch: A Study of Provincial Life. The last part appears in 1872. |
| 1871 | England [scientific publications] | English naturalist Charles Darwin publishes The Descent of Man, and Selection in Relation to Sex, in which he applies his evolutionary theory to humans and also elaborates the theory of sexual selection. |
| 1871 | Germany, USA, France, Japan, UK, Ireland, Italy [statistics and demography] | Populations of selected countries (in millions): Germany, 41; USA, 39; France, 36.1; Japan, 33; Great Britain, 26; Ireland, 5.4; Italy, 26.8. |
| 18 January 1871 | Prussia, Germany [political events] | Following the defeat of Emperor Napoleon III of France in the Franco-Prussian War, King Wilhelm I of Prussia is proclaimed German emperor at Versailles in France, the North German Confederation having been enlarged to include all the German states except Austria-Hungary. |
| 28 January 1871 | France, Germany [Franco–Prussian War (1870–71)] | The French capital, Paris, besieged by Prussian forces since September 1870, capitulates and an armistice with Germany is signed. |
| 13 March 1871 | Russian Empire, Europe [treaties] | The London Conference between the great powers of Europe revokes the Black Sea clauses of the Treaty of Paris of 1856 and gives Russia the freedom to deploy its forces in the Black Sea (following Russia's independent repudiation of these clauses in October 1870). |
| 18 March 1871 | France [Franco–Prussian War (1870–71)] | A left-wing rising begins in Paris, France, when soldiers sent to requisition cannons stationed in the city side with the populace, who wish to establish their own radical government and continue the war with Prussia. |
| 10 May 1871 | France, Prussia, Germany [treaties] | The Peace of Frankfurt formally ends the Franco-Prussian War. France is to cede Alsace-Lorraine to Germany, pay an indemnity of 5 milliards of francs, and be subject to military occupation until payment is completed. |
| 21 May - 28 May 1871 | France [political events] | In ‘Bloody Week’ in Paris, France, fighting between government troops and demonstrators ends in the defeat of the extreme left-wing Paris Commune (provisional national government) at a cost of 20,000–30,000 lives. |
| 29 May 1871 | UK [work and unemployment] | Bank holidays are introduced in England, Wales, and Ireland, with the first on Whit Monday (the first Monday after Pentecost). |
| 7 July 1871 | Germany [Catholicism] | The German government begins its Kulturkampf (cultural struggle) with the Catholic Church, when Chancellor Otto von Bismarck suppresses the Roman Catholic department for spiritual affairs. |
| 10 July 1871 | France [births and deaths] | Marcel Proust, French novelist who writes A la recherche du temps perdu/Remembrance of Things Past (1913–27), born in Auteuil, France (–1922). |
| 19 August 1871 | USA [births and deaths] | Orville Wright, US pioneer of aviation who, with his brother Wilbur, is the first to achieve sustained powered flight, born in Dayton, Ohio (–1948). |
| 30 August 1871 | New Zealand [births and deaths] | Ernest Rutherford, New Zealand physicist and investigator of radioactivity, born in Spring Grove, New Zealand (–1937). |
| 31 August 1871 | France [elections] | The French Liberal statesman Adolphe Thiers is elected the first president of the Third Republic in France. |
| 18 October 1871 | England [births and deaths] | Charles Babbage, English inventor who designed the first digital computer, dies in London, England (78). |
| 23 October 1871 - 14 March 1872 | Africa [exploration] | Welsh-born US journalist Henry Stanley reaches Lake Tanganyika in Africa in search of the lost Scottish explorer David Livingstone, who he finds at the trading settlement of Ujiji. Together they explore the lake's northern reaches, and establish that it is not the source of the Nile. Livingstone refuses to leave Africa with Stanley. |
| 1 November 1871 | USA [births and deaths] | Stephen Crane, US novelist known for his book The Red Badge of Courage (1895), born in Newark, New Jersey (–1900). |
