Charles Fort: A Fortean Chronology, 1913.

Peter Kurten, who would become known as 'The Vampire of Dusseldorf' and inspiration for the killer in Fritz Lang's 1931 film 'M', committed his first provable murder in 1913, strangling a 10-year-old girl, Christine Klein, during the course of a burglary.

January

• January 4: An unknown airship is seen over Dover, England. (Books512)
• January 13: The Irish Ulster Volunteers are reorganized into the Ulster Volunteer Force (UVF) by the Ulster Unionist Party, with the intention of defending Ulster against Home Rule.
• January 17: An object is seen in the sky leaving a trail of dense smoke over Cardiff, Wales. (Books513)
• January 23: Coup of 1913 in the Ottoman Empire: The CUP, lead by Enver Pasha, overthrows the Liberal Union coalition and introduces a military dictatorship.
• January 24: Brilliant lights are seen over Tottertown, Wales; a 'searchlight' illuminating the surrounding hills. (Books513)
• January 30: The House of Lords rejects the third Irish Home Rule Bill.

February

• February 1: New York City's Grand Central Terminal, having been rebuilt, reopens as the world's largest train station.
• February 4: The trial of the remnants of the Bonnot Gang begins in France.
• February 9: The Great Fireball Procession, a chain of slow, large meteors moving from northwest to southeast, is sighted over North America, particularly in Canada. (Books296)
• February 21: Luminous objects are seen over English towns from Yorkshire to Warwickshire. (Books514)
• February 24: A bright light, appearing and disappearing, is seen over Portsmouth for about an hour before moving away. (Books515) 

March

• The House of Romanov celebrates the 300th anniversary of their succession to the throne, amidst an outpouring of monarchist sentiment in Russia.
• March 4: Woodrow Wilson succeeds William Howard Taft as the 28th President of the United States.
• March 5-7: First Battle of Bud Dajo, American troops decisively defeat Moro rebels in the Philippines.
• March 7: The British freighter Alum Chine, carrying 343 tons of dynamite, explodes in Baltimore harbour.
• March 12: Australia begins building the new federal capital of Canberra.
• March 13: Mexican Revolution, Pancho Villa returns to Mexico from his self-imposed exile in the United States.
• March 18: King George I of Greece is assassinated.
• March 25: Mexican Revolution, Venustiano Carranza announces his Plan of Guadalupe, and begins his rebellion against Victoriano Huerta's government as head of the Constitutionals.
• March 25: Two days of rain in the Miami Valley flood the region and mark the worst natural disaster in Ohio's recorded history. Dayton is especially devastated in this great flood. (Books753)
• March 26: Balkan War: Bulgarian forces take Adrianople.

April

• April 8: Captain Lindsay reports that he and many other people observed, over Cardiff, Wales, something that carried a brilliant light and travelled at a rate of sixty or seventy miles an hour. (Books515)
• April 20: A huge, unknown animal, is seen near Macquarie Harbour, Tasmania. (Books623)
• April 24: The Woolworth Building opens in New York City.
• April 26: Mary Phagan is raped and strangled on the premises of the National Pencil Factory in Atlanta. Leo Frank is tried and convicted for the crime.
• April 29: Swedish engineer Gideon Sundback of Hoboken patents all-purpose zipper.

May

• May 14:  New York Governor William Sulzer approves the charter for the Rockefeller Foundation, which begins operations with a $100,000,000 donation from John D. Rockefeller.
• May 29: Igor Stravinsky's ballet score The Rite of Spring premieres in Paris, causing a riot that very night.
• May 30: First Balkan War, A peace treaty is signed in London, ending the war.

June

• June 4: Emily Davison, a British suffragette, runs out in front of the King's horse, Anmer, at the Epsom Derby. She is trampled and dies 4 days later in the hospital, never having regained consciousness.
• June 13: A Great Gorge and International Railway trolley and passengers are buried under the contents of an overhead garbage chute, that breaks in Niagara Falls, New York.
• June 15: Bud Bagsak Massacre: U.S. troops under General John 'Black Jack' Pershing kill at least 2,000 civilians in Bud Bagsak, the Philippines.

July

• July 9: In Paris, France, a wealthy engineer named Leramgourg is arrested. "At Leramgourg's residence, the police found locks of hair of 94 women." (Books871) 

August

• August 4: In China, the province of Chungking declares independence; Chinese Republican forces crush the rebellion in a couple of weeks.
• August 10: Macedonia is divided after the Second Balkan War, according to the Treaty of Bucharest.
• August 13: Stainless steel is invented by Harry Brearley in Sheffield.
• August 15: The Dublin Strike & Lockout begins; all trade union members are dismissed.

September

• September 29: Rudolf Diesel disappears en route to Britain.
• September 29: Mexican Revolution, Pancho Villa is elected commander of the "Northern Division" of the Constitutionals.

October

• October 1: Mexican Revolution, Pancho Villa's troops take Torreón after a 3-day battle, when government troops retreat.
• October 9: SS Volturno catches fire and sinks in the North Atlantic
• October 10: U.S. President Woodrow Wilson triggers the explosion of the Gamboa Dike, ending construction on the Panama Canal.
• October 13: Albert Jewell "was completely lost as if he had evaporated into air," whilst attempting to fly his aeroplane from Hempstead Plains, Long Island, to Staten Island. (Books521)
• October 31: The Lincoln Highway, the first automobile road across the United States, is dedicated.

November

• November 1: Panama Canal employees reach their highest number (56,654) since construction began in 1904.
• November 5: The insane King Otto of Bavaria is deposed by his cousin, Prince Regent Ludwig, who assumes the title Ludwig III.
• November 6: Mohandas Gandhi is arrested while leading a march of Indian miners in South Africa.
• November 7-11: The Great Lakes Storm of 1913 kills more than 250.

December

• December 1: The Ford Motor Company introduces the first moving assembly line, reducing chassis assembly time from 12½ hours in October to 2 hours, 40 minutes.
• December 1: Crete, having obtained self rule from Turkey after the first Balkan War, is annexed by Greece.
• December 4: Mrs Wesley Graff, sat in a box at the Lyric theatre, New York City, collapsed when she was 'jabbed' in the arm. A darning needle is found nearby, but the wounds upon Mrs Graff's arm were not made by such a needle. (Books885) 
• December 12: Emperor of Ethiopia Menelik II dies and is succeeded by his grandson Iyasu V of Ethiopia.
• December 12: Vincenzo Perugia tries to sell the Mona Lisa in Florence and is arrested.
• December 21: Arthur Wynne's "word-cross", the first crossword puzzle, is published in the New York World.
• December 23: The Federal Reserve is created by Woodrow Wilson.
• December 30: Italy returns the Mona Lisa to France.