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1886 (MDCCCLXXXVI) was a common year starting on Friday of the Gregorian calendar and a common year starting on Wednesday of the Julian calendar, the 1886th year of the Common Era (CE) and Anno Domini (AD) designations, the 886th year of the 2nd millennium, the 86th year of the 19th century, and the 7th year of the 1880s decade. As of the start of 1886, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.
- April 4 – William Ewart Gladstone introduces the First Irish Home Rule Bill in the Parliament of the United Kingdom; it is defeated on June 8.
- April 6 – The settlement of Vancouver, British Columbia is incorporated.
- April 24 – Father Augustine Tolton, the first Roman Catholic priest from the United States to identify himself publicly as African American, is ordained in Rome.
- April 25 – Easter occurs on the latest possible date (the next time is in 1943).
- April – The Swedish Dress Reform Society is established.
- May 1 – A general strike begins in the United States, which escalates on May 4 into the Haymarket affair in Chicago, and eventually wins the eight-hour day for workers.
- May 4 – Emile Berliner starts work that leads to the invention of the gramophone.
- May 8 – American pharmacist Dr. John Pemberton invents a carbonated beverage that will be named 'Coca-Cola'.
- May 15 – Portugal and France agree to regulate the borders of their colonies in Guinea.
- May 17
- May 29 – John Pemberton begins to advertise Coca-Cola (in The Atlanta Journal).
- June 2 – U.S. President Grover Cleveland marries Frances Folsom in the White House (Washington, D.C.), becoming the only President of the United States to wed in the executive mansion. She is 27 years his junior.
- June 3 – Uganda Martyrs: Charles Lwanga, 12 other Catholic boys and men, and 9 Anglicans, are burned (and another Catholic speared) to death, at the orders of Kabaka Mwanga II of Buganda in Namugongo.
- July 3 – Karl Benz officially unveils the Benz Patent Motorwagen.
- July 9 – American inventor Charles M. Hall files a patent for his inexpensive method of refining aluminium (discovered on February 23); independently and near-simultaneously discovered in France by Paul Héroult it becomes known as the Hall–Héroult process.
- July 23 – Steve Brodie is reported to have made a jump from the Brooklyn Bridge, a claim subsequently disputed.
- July 25 – Robert Cecil, 3rd Marquess of Salisbury (Conservative Party (UK)) becomes Great Britain's 30th Prime Minister.
- August 13 – Nagasaki Incident: Chinese troops riot during shore leave in Nagasaki, Japan.
- August 19 – The Christian Union (Church of God) is established.
- August 20 – A massive hurricane demolishes the town of Indianola, Texas.
- August 31 – The 7.0 Mw Charleston earthquake affects southeastern South Carolina, with a maximum Mercalli intensity of X (Extreme); 60 people are killed, and damage is estimated at $5–6 million.
- September 1 – Grasshopper Club Zürich is founded as the first football club in the Swiss city of Zürich by English students.
- September 4 – American Indian Wars: After almost 30 years of fighting, Apache leader Geronimo surrenders, with his last band of warriors, to General Nelson Miles, at Skeleton Canyon in Arizona.
- September 9 – The Berne Convention for the Protection of Literary and Artistic Works is signed.
- September 21 – American physicist William Stanley, Jr. patents the first practical alternating current transformer device, the induction coil.
- October 7 – Spain abolishes slavery in Cuba.
- October 28 – In New York Harbor, U.S. President Grover Cleveland dedicates the Statue of Liberty, a gift from France. The ensuing spontaneous celebration in New York City leads to the first ticker tape parade.
- November – The extremely harsh winter of 1886–87 in the United States begins, killing tens of thousands of cattle on the Great Plains of North America.
- November 1 – The biggest Buddhist boys' school in Sri Lanka, Ananda College, is founded in Colombo.
- November 3 – In the British Raj, what will become one of the biggest boys' schools in Pakistan, Aitchison College, Lahore, is founded under the auspices of Sir Charles Umpherston Aitchison.
- November 11 – Heinrich Hertz verifies the existence of electromagnetic waves, at the University of Karlsruhe.
- November 14 – German inventor Friedrich Soennecken first develops the hole puncher, a type of office tool capable of punching small holes in paper.
- November 30 – The Folies Bergère stages its first revue in Paris.
- December 11 – London club Arsenal, founded as Dial Square by workers at the Royal Arsenal in Woolwich, play their first match (on the Isle of Dogs). The club is renamed Royal Arsenal soon afterwards, supposedly on December 25.
- December 17 – English adventurer Thomas Stevens concludes the first circumnavigation by bicycle in Yokohama, having set out on his penny-farthing from San Francisco in 1884.