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1975–1980: Magician

Producers Richard D. Zanuck and David Brown took a chance with Spielberg, and gave him the opportunity to direct Jaws (1975), a horror-thriller based on Peter Benchley 's novel of the same name. In it, a great white shark attacks beachgoers at a summer resort town, prompting police chief Martin Brody (Roy Scheider) to hunt it down with the help of a marine biologist (Richard Dreyfuss) and a veteran shark hunter (Robert Shaw). Jaws was the first movie shot on open ocean, so shooting proved difficult, and the mechanical shark malfunctioned. The filming schedule overran by a hundred days, and Universal threatened to cancel production. Against expectations, Jaws was a success; it set the domestic box office record, making Spielberg a household name. It won Academy Awards for Best Film Editing (Verna Fields), Best Original Dramatic Score (John Williams) and Best Sound (Robert Hoyt, Roger Heman, Earl Madery and John Carter). Spielberg said the malfunctioning of the mechanical shark resulted in a better movie, as he had to find other ways to suggest the shark's presence. After seeing the unconventional camera techniques of Jaws, Alfred Hitchcock praised "young Spielberg" for thinking outside the visual dynamics of the theater: "He's the first one of us who doesn't see the proscenium arch".

After the success of Jaws, Spielberg declined an offer to make Jaws 2. He and Richard Dreyfuss re-convened to work on a film about UFOs, Close Encounters of the Third Kind (1977). During filming, Spielberg used 65 mm film for the best picture quality, and a new live-action recording system so that the recordings could be duplicated later. He cast one of his favorite directors, François Truffaut, as the scientist Claude Lacombe and worked with special effects expert Douglas Trumbull. One of the rare films both written and directed by Spielberg, Close Encounters was very popular with film-goers, and he received his first Best Director nomination from the Academy Awards. It earned six more nominations, winning Best Cinematography (Vilmos Zsigmond) and Best Sound Effects Editing (Frank Warner). Stanley Kauffmann wrote: "I saw Close Encounters at its first public showing in New York, and most of the audience stayed on and on to watch the credits crawl lengthily at the end. For one thing, under the credits the giant spaceship was returning to the stars. For another, they just didn’t want to leave this picture. For still another, they seemed to understand the importance of those many names to what they had just seen." Kauffmann placed it first on his list of the best American films from 1968 to 1977. Reviewing Close Encounters, Kael called Spielberg "a magician in the age of movies."

Spielberg's first film as an executive producer was the directorial debut of Robert Zemeckis, I Wanna Hold Your Hand (1978). His next directorial work was 1941 (1979), an action-comedy written by Zemeckis and Bob Gale about Californians preparing for a Japanese invasion after the attack on Pearl Harbor. Spielberg was self-conscious about doing comedy as he had no prior experience in the genre. Universal and Columbia agreed to co-finance the film. 1941 grossed over $92.4 million worldwide upon release, but most critics, and the studio heads, disliked it. Charles Champlin described 1941 as "the most conspicuous waste since the last major oil spill, which it somewhat resembles." Stanley Kubrick supposedly said that the film was "great, but not funny."