George Lucas wrote the story treatment for the entire saga alone and the script for the first film (relabeled A New Hope) was a solo effort.
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According to the New Hope page:
• In January 1973 Lucas began work on (The Adventures of Luke Starkiller), and by May had prepared a 14-page story outline for distribution among film studios.
• Lucas finished a draft of the screenplay in May 1974. As the draft developed, the characters evolved significantly.
• The completed script was too long for one movie; however, Lucas refused to condense it. Instead, he expanded the first third of it into one movie and left the rest for two future films, effectively creating the original Star Wars trilogy.
Regarding The Empire Strikes Back
• Lucas hired screenwriter Leigh Brackett to write a screenplay based on his story treatment. Brackett finished the first draft on February 23, 1978 but she died soon afterward. According to Lucas, he didn't like the direction in which her screenplay went. Without a writer to fix it, he was forced to write the second draft himself throughout March. Major plot changes were made compared to the first draft and the storyline that is in the film was formed in this draft. One of the most notable changes was making Vader Luke's father. When Lawrence Kasdan finished writing the screenplay for Raiders of the Lost Ark he was hired to rewrite and improve Lucas' draft. He wrote a few more drafts before the script conference was held in November between George Lucas, Lawrence Kasdan, Irvin Kershner and Gary Kurtz. After some additional input, the shooting script was finally formed. Minor changes to dialogues came from Kershner and actors throughout the filming and were mostly approved by Lucas.
• For Return of the Jedi, the screenplay was written by Lawrence Kasdan and Lucas (with uncredited contributions by David Webb Peoples), based on Lucas's story.