The year 1877 in science and technology involved some significant events, listed below.

• June 19 – Eadweard Muybridge successfully produces a fast-motion sequence of photographs showing a horse in movement, Sallie Gardner at a Gallop, using multiple cameras at Palo Alto, California, demonstrating that a running horse has all four legs lifted off the ground at once. The sequence could be run on a Zoopraxiscope.^[1]

• August 12 – American astronomer Asaph Hall discovers Deimos, the smaller of the two moons of Mars. On August 18, he discovers the larger, Phobos.

• Peirce quincuncial projection devised by Charles Sanders Peirce.^[2]

• Ludwig Boltzmann establishes statistical derivations of many important physical and chemical concepts, including entropy, and distributions of molecular velocities in the gas phase.^[3]

• June 26 – Volcanic eruption of Cotopaxi in Ecuador.

• Dr. August Eisenlohr publishes the first translation and study of the Rhind Mathematical Papyrus.^[4]
• American railroad lawyer and ethnologist Lewis H. Morgan publishes Ancient Society, linking social progress with technological change.

• Georg Cantor advances the continuum hypothesis.

• October 2 – Berlin urologist Maximilian Nitze and Viennese instrument-maker Josef Leiter introduce the first practical cystourethroscope with an electric light source.^[5]
• Adolph Kussmaul first describes dyslexia as "word-blindness".
• William Macewen at the Glasgow Royal Infirmary develops the first bone grafts, and also performs knee surgery using a special instrument (Macewen's osteotome), for the treatment of rickets.
• Patrick Manson studies animal carriers of infectious diseases.

• Ludwig Boltzmann states the relationship between entropy and probability.

• March 28 – Frederick Wolseley is granted his first patent for a sheep shearing machine.
• April 30 – French poet Charles Cros describes a method of recording sound, the Paleophone.
• June – Emile Berliner files a patent for a "combined telegraph and telephone" incorporating a microphone.^[6]
• June 20 – Alexander Graham Bell installs the world's first commercial telephone service in Hamilton, Ontario.
• September 4 – Louis Brennan patents the Brennan torpedo.
• October – Emile Berliner files a patent for a telephone with induction coils.^[7]
• November 4 – Opening of Gustave Eiffel's Maria Pia Bridge carrying the railway across the Douro into Porto, Portugal.
• November 29 – Thomas Edison first demonstrates his phonograph sound recording machine.
• December 13 – Thomas Edison files a patent for "telephones or speaking-telegraphs" incorporating a microphone.^[8]
• Surveyor and inventor George R. Carey of Boston, Massachusetts, creates a selenium telectroscope — a camera that can project a moving image to a distant point, an ancestor of television. Constantin Senlecq of Ardres, France, develops the same idea independently at about the same time.^[9]

• Zeitschrift für Physiologische Chemie is founded by Felix Hoppe-Seyler.

• Copley Medal: James Dwight Dana^[10]
• Wollaston Medal: Robert Mallet

• February 2 – Margarete Zuelzer (died 1944), German microbiologist.
• February 7 – G. H. Hardy (died 1947), English mathematician.
• March 16 – Thomas Wyatt Turner (died 1978), American civil rights activist, biologist and educator; first black person ever to receive a doctorate from Cornell.
• April 5 – Walter Sutton (died 1916), American geneticist and surgeon.
• April 24 – José Ingenieros (died 1925), Argentine polymath.
• June 14 – Ida Maclean, born Ida Smedley (died 1944), English biochemist.
• September 1 – Francis William Aston (died 1945), English chemist, Nobel Prize laureate.
• September 2 – Frederick Soddy (died 1956), English physical chemist.
• September 11 – James Hopwood Jeans (died 1946), English mathematician.
• September 13 – Wilhelm Filchner (died 1957), German explorer.
• October 21 – Oswald Avery (died 1955), Canadian American bacteriologist.
• October 25 – Henry Norris Russell (died 1957), American astronomer.
• November 3 – Rosalie Edge (died 1962), American conservationist.

• January 2 – Alexander Bain (born 1810), Scottish inventor.
• January 12 – Wilhelm Friedrich Benedikt Hofmeister (born 1824), German botanist.
• February 8 – Charles Wilkes (born 1798), American navigator.
• April 9 – Pierre Louis Alphée Cazenave (born 1795), French dermatologist.
• May 5 – Joseph Bienaimé Caventou (born 1795), French pharmacist.
• June 3 – Ludwig von Köchel (born 1800), Austrian musicologist and botanist.
• September 17 – H. Fox Talbot (born 1800), English pioneer of photography.
• September 23 – Urbain Le Verrier (born 1811), French astronomer.
• September 26 – Hermann Günther Grassmann (born 1809), German mathematician.
• Choe Han-gi (born 1803), Korean philosopher of science.