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1875 (MDCCCLXXV) was a common year starting on Friday of the Gregorian calendar and a common year starting on Wednesday of the Julian calendar, the 1875th year of the Common Era (CE) and Anno Domini (AD) designations, the 875th year of the 2nd millennium, the 75th year of the 19th century, and the 6th year of the 1870s decade. As of the start of 1875, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 1 – The Midland Railway of England abolishes the Second Class passenger category, leaving First Class and Third Class. Other British railway companies follow Midland's lead during the rest of the year (Third Class is renamed Second Class in 1956).
- January 5 - The Palais Garnier, one of the most famous opera houses in the world, is inaugurated in Paris.
- January 12 – Guangxu becomes the 11th Qing Dynasty Emperor of China at the age of 4, in succession to his cousin.
- January 14 – The newly proclaimed King Alfonso XII of Spain (Queen Isabella II's son) arrives in Spain to restore the monarchy during the Third Carlist War.
- February 3 – Third Carlist War – Battle of Lácar: Carlist commander Torcuato Mendíri secures a brilliant victory, when he surprises and routs a Government force under General Enrique Bargés at Lácar, east of Estella, nearly capturing newly crowned King Alfonso XII. The Carlists take several pieces of artillery, more than 2,000 rifles, and 300 prisoners. 800 men of both sides are killed (mostly government troops).
- February 18 – The Mason County War begins, as a German-American mob breaks into a prison, and lynches cattle rustlers in central Texas.
- February 21 – Jeanne Calment is born in Arles, France. She will go on to become the world's oldest verified person to have ever lived, reaching an age of 122 years and 164 days, before passing away on August 4, 1997 of natural causes.
- February 24 – The SS Gothenburg sinks off Australia's east coast with the loss of approximately 102 lives, including a number of high-profile civil servants and dignitaries.
- February 25 – The majority of the Yavapai (Wipukyipai) and Tonto Apache (Dil Zhéé) tribes are forced by the United States Cavalry, under command of Brigadier General George Crook, to walk at gunpoint from the Arizona's Verde Valley, to the San Carlos Apache Indian Reservation, 180 miles to the southeast. The two tribes are not allowed to return to the Verde Valley until 1900.
- February 27 – Newton Booth, 11th Governor of California, resigns, having been elected Senator. Lieutenant Governor of California Romualdo Pacheco becomes acting Governor. He is later replaced by elected governor William Irwin.
- March 1 – The United States Congress passes the Civil Rights Act, which prohibits racial discrimination in public accommodations and jury duty.
- March 3
- March 15 – Roman Catholic Archbishop of New York John McCloskey is named the first cardinal in the United States.
- Summer – Third Carlist War in Spain: Two government armies under General Quesada and Martínez Campos start encroaching on Carlist territory. Both they and their Carlist opponent (Mendiri) drive opposing sympathisers from their homes, and burn crops in areas they can not hold. Several Carlist generals (Dorregaray, Savalls, and others) are unjustly put on trial for disloyalty. Mendiri is also removed from his command, and replaced by the Count of Caserta. Despite having 48 infantry battalions, 3 cavalry regiments, 2 engineer battalions, and 100 pieces of artillery at his disposal, Caserta is heavily outnumbered by the government forces opposing him.
- July 1 – The General Postal Union is established.
- July 1–7 – Third Carlist War – Battle of Treviño: Advancing on the key city of Vitoria, in Navarre, Spanish Republican commander General Jenardo de Quesada sends General Tello to attack the Carlist lines just to the southwest, at Treviño. The newly appointed Carlist commander General José Pérula is heavily defeated and withdraws, and soon afterwards Quesada enters Vitoria in triumph.
- July 24 – The Mohican Base Ball Club is established in Kennett Square, PA.
- August 6 – Hibernian F.C. is founded by Irishmen, in the Cowgate area of Edinburgh, Scotland.
- August 25 – Captain Matthew Webb becomes the first person to swim the English Channel.
- September 1 – A murder conviction begins to break the power of the violent Irish-American anti-owner coal miners, the "Molly Maguires".
- September 7 – Battle of Agurdat: An Egyptian invasion of Ethiopia fails, when Emperor Yohannes IV defeats an army led by Werner Munzinger.
- September – English team Birmingham City F.C. is founded as Small Heath Alliance in Birmingham by a group of cricketers from Holy Trinity Church, Bordesley, playing its first match in November.
- October – The Ottoman state declares partial bankruptcy, and places its finances in the hands of European creditors.
- October 15 – Chief Lone Horn of the Minneconjou dies at the Cheyenne River, leaving his son Big Foot as the new chief.
- October 16 – Brigham Young University is founded in Provo, Utah.
- October 25 – The first performance of the Piano Concerto No. 1 by Pyotr Ilyich Tchaikovsky is given in Boston, Massachusetts, with Hans von Bülow as soloist.
- October 30 – The Theosophical Society is founded in New York by Helena Blavatsky, H. S. Olcott, W. Q. Judge, and others.
- November 9 – American Indian Wars: In Washington, D.C., Indian Inspector E.C. Watkins issues a report stating that hundreds of Sioux and Cheyenne associated with Sitting Bull and Crazy Horse are hostile to the United States (the Battle of the Little Bighorn is fought in Montana the next year).
- November 16 – Battle of Gundat: Ethiopian Emperor Yohannes IV defeats another Egyptian army.
- November 26 – The Times newspaper in London reveals that Isma'il Pasha has sold Egypt's 44% share in the Suez Canal to Britain, in a deal secured by Benjamin Disraeli, without the prior sanction of the British Parliament.
- December 4 – Notorious New York City politician Boss Tweed escapes from prison and flees to Cuba, then to Spain.
- December 5–6 – German emigrant ship SS Deutschland runs aground in the English Channel, resulting in the death of 157 passengers and crew.
- December 9 – The Massachusetts Rifle Association, America's Oldest Active Gun Club, is formed.
- December 20 – The ICRM is renamed the International Committee of the Red Cross (ICRC).
- December 25 – The first Edinburgh derby in is played: Heart of Midlothian F.C. wins 1–0 against Hibernian F.C.
- Asia's first stock exchange is established as The Native Share & Stock Brokers Association, (the modern-day Bombay Stock Exchange).
- Wimbledon: Henry Cavendish Jones convinces the All England Croquet Club to replace a croquet court with a lawn tennis court.
- The Artisans' and Labourers' Dwellings Improvement Act 1875 is passed in the United Kingdom, to permit slum clearance.
- Widespread nationalist rebellion in the Ottoman Empire results in Turkish repression, Russian intervention and Great Power tensions.
- Convent Scandal: During the winter in Montreal, typhoid fever strikes at a convent school. The corpses of the victims are filched by body-snatchers before relatives arrive from America, causing much furor. Eventually the Anatomy Act of Quebec is changed over it.
- The opening of Flushing High School, the oldest public high school in New York City.
- Tanaka Manufacturing, a telecommunications factory in Ginza, Tokyo, a predecessor of Toshiba, a Japanese giant electromechanics is founded.