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Top Song(s)
• The Kingston Trio - Tom Dooley
• Domenico Modugno - Volare
• The Kalin Twins - When
• The Everly Brothers - All I Have to Do is Dream
• Champs - Tequila
Top Film(s)
• Touch of Evil
• Vertigo
• The Hidden Fortress
• Elevator to the Gallows
• Cat on a Hot Tin Roof
Best Selling Book(s)
• Things Fall Apart - Chinua Achebe
• Breakfast at Tiffany’s and Three Stories - Truman Capote
• The Witch of Blackbird Pond - Elizabeth George Speare
• The Cat in the Hat Comes Back - Dr. Seuss
• The Once and Future King - T.H. White
Famous Deaths
• January 7 – Petru Groza, Romanian politician, 46th Prime Minister of Romania
• March 11 – Ole Kirk Christiansen, Danish businessman, founder of The Lego Group
• April 8 – Alcibiades Arosemena, Panamanian politician, 15th President of Panama
• May 29 – Juan Ramón Jiménez, Spanish writer, Nobel Prize laureate
• June 16 - Nereu Ramos, Brazilian politician, 20th President of Brazil
• July 18 – Henri Farman, French aviator and aircraft company founder
• August 24 – J. G. Strijdom, 5th Prime Minister of South Africa
• October 14 – Sir Douglas Mawson, Australian geologist and polar explorer
• November 24 – Robert Cecil, 1st Viscount Cecil of Chelwood, English politician and diplomat
• December 12 - Milutin Milankovic, Yugoslav mathematician, astronomer, climatologist and geophysicist
Medical/Science/Technology
• Sputnik 1 falls to Earth from its orbit and burns up.
• The first successful American satellite, Explorer I, is launched into orbit.
• Explorer 3 is launched into orbit.
• Francis Crick states the "central dogma of molecular biology".
• John Gurdon clones a frog using somatic-cell nuclear transfer from a Xenopus tadpole.
• Denatonium, the bitterest chemical compound known (used as an aversive agent), is discovered.
• Jerome Lejeune, discovers that the genetic cause of Down syndrome is an extra copy of chromosome 21.
• Ian Donald publishes an article in The Lancet which describes the diagnostic use of ultrasound in obstetrics.
• Denis Parsons Burkitt first describes Burkitt's lymphoma.
• Fritz Heider proposes the naïve scientist model of social cognition.
Political
• March 26 - The United States Army launches Explorer 3.
• May 12 – A formal North American Aerospace Defense Command agreement is signed between the United States and Canada.
• May 22 – U.S. President Dwight D. Eisenhower becomes the first American elected official to appear on color television.
• June 17 – The U.S. condemns the execution of Imre Nagy as a "shocking act of cruelty".
• July 3 – 1958 US–UK Mutual Defense Agreement signed in Washington, D.C.
• July 7 – President Dwight D. Eisenhower signs the Alaska Statehood Act into United States law.
• July 24 – Fourteen life peerages, the first under the Life Peerages Act 1958, are created in the United Kingdom.
• July 29 – The U.S. Congress formally creates the National Aeronautics and Space Administration (NASA).
• August 23 – President Dwight D. Eisenhower signs the Federal Aviation Act of 1958.
• December 19 – A message from President Dwight D. Eisenhower is broadcast from SCORE, first communications satellite.
National
• January 8 – Bobby Fischer, 14 years old at the time, wins the United States Chess Championship.
• January 18 - Battle of Hayes Pond: Armed Lumbee Indians confront the Ku Klux Klan in Maxton, North Carolina.
• January 31 – The first successful American satellite, Explorer 1, is launched into orbit.
• March 11 – A U.S. B-47 bomber accidentally drops an atom bomb on Mars Bluff, South Carolina.
• May 22 – First color television switch WRC-TV dedication.
• June 8 – The SS Edmund Fitzgerald is launched; it will be the largest freighter on the Great Lakes.
• June 15 – The first Pizza Hut restaurant opens in Wichita, Kansas.
• September 15 – Newark Bay rail accident kills 48 people and injures the same number.
• October 1 – NASA starts operations and replaces the National Advisory Committee for Aeronautics.
• November 20 – The Jim Henson Company is founded as Muppets, Inc.
Worldwide
• February 1 – Egypt and Syria unite, to form the United Arab Republic.
• February 17 – Bertrand Russell launches the Campaign for Nuclear Disarmament in the UK.
• March 27 – Nikita Khrushchev becomes Premier of the Soviet Union.
• May 1 - Arturo Frondizi becomes President of Argentina.
• June 30 – The Ifni War ends in Spanish Sahara.
• August 26 – A general strike is called in Paraguay.
• August 30 – September 1 – Notting Hill race riots: Riots occur between blacks and whites in Notting Hill, London.
• September 14 – Two rockets designed by German engineer Ernst Mohr reach the upper atmosphere.
• October – GoldStar, as predecessor for LG Electronics, founded in South Korea.
• December 31 – After the fall of Santa Clara, Cuban President Fulgencio Batista flees the country.