Short answers, pulled from the story.
Sergei Eisenstein is best known for his silent films Strike (1925), Battleship Potemkin (1925), and October (1928), as well as his foundational contributions to montage theory. Sight and Sound magazine named Battleship Potemkin the 54th-greatest film of all time in its decennial poll.
Montage theory is the idea that the juxtaposition of two independent film shots creates a third meaning that exists in neither image alone. Eisenstein developed this through his writings, particularly Film Form and The Film Sense, and distinguished five methods of montage: metric, rhythmic, tonal, overtonal, and intellectual. He contrasted his "collision" approach with the "linkage" model of his contemporary Lev Kuleshov.
Eisenstein signed a contract on the 24th of November 1930 with Upton Sinclair's Mexican Film Trust to make a film titled Que viva Mexico!, but production ran far over schedule and budget. Sinclair shut it down and the footage, estimated at between 170,000 and over 250,000 lineal feet, was taken to the United States. Sol Lesser produced two short feature films and a short subject from the material, none of which Eisenstein ever saw.
Paramount cancelled its contract with Eisenstein on the 23rd of October 1930, citing dissatisfaction with his script for Theodore Dreiser's An American Tragedy and public pressure from Major Pease, president of the Hollywood Technical Director's Institute, who led an anti-communist campaign against him. The studio declared the contract null and void by mutual consent and paid for the Eisenstein party's return tickets to Moscow.
Eisenstein received two Stalin Prizes: the first in 1941 for Alexander Nevsky (1938) and the second in 1946 for Ivan the Terrible Part I (1944). He also received the Order of Lenin in 1939 for Alexander Nevsky, the Order of the Badge of Honour, and the title Honored Artist of the RSFSR in 1935.
Eisenstein died of a heart attack on the 11th of February 1948, at the age of 50. He had suffered a first heart attack on the 2nd of February 1946 and spent much of the following year recovering. His ashes were buried in the Novodevichy Cemetery in Moscow.