Asimov was first contacted by Leon Svirsky of Basic Books in 1959 about the possibility of writing a book that would provide an overview of science, and the two met at Asimov's home on 13 May to discuss the details. Six days later, Asimov received a contract for the book, along with a $1500 advance. At this point in his life, it had been just over a year since Asimov had given up his teaching duties at Boston University and taken up writing full-time. He had published 11 nonfiction books, including books on chemistry, physics, astronomy, a college-level biochemistry textbook, and a collection of science essays. However, he was momentarily daunted by the prospect of writing a major book on all of science, and he delayed signing the contract until 15 July, after receiving encouragement from his friend (and future wife) Janet Jeppson.
The book's title was Svirsky's, chosen as a deliberate homage to George Bernard Shaw's The Intelligent Woman's Guide to Socialism and Capitalism (1928). Asimov feared the title would be seen as elitist and condescending, and he suggested Everyone's Guide to Science as an alternative, but Svirsky refused. Years later, when he was confronted by annoyed feminists who asked why the book was restricted to men, Asimov would claim that the "intelligent man" of the title referred to himself; thus anticipating the title Asimov's Guide to Science adopted for the third edition. Svirsky also wanted the book confined to scientific advances made in the 20th century. Asimov, however, preferred to approach each field in a historical manner, starting with the ancient Greeks or, at the very least, Galileo Galilei. As often happened when Asimov was given editorial directions he disagreed with, he ignored them, and wrote the book just as he wanted to. In organizing the various fields of science, Asimov chose to begin with the universe as a whole and work inward in narrowing circles until he was inside the brain at the end.
Asimov began work on the book on 2 October, and found that he had no trouble with it at all, writing anywhere from 6000 to 10,000 words a day without any sense of strain. By 27 January 1958, Asimov was able to deliver the first half of the completed manuscript to Basic Books, but at a meeting a month later, Svirsky suggested cutting the book in half so it could fit in one volume. At that point, Asimov was only two chapters shy of finishing the book, but saw no reason to complete it if it would be subjected to such radical abridgment, and halted work. He resumed work after being informed on 11 March that Svirsky would not try to reduce the book by half, but would instead publish it in two volumes. Svirsky also insisted that the book include an introduction by the geneticist George Beadle. Asimov felt that his work didn't need an introduction by anyone else, and even though he found Beadle's introduction to be very elegant, he still resented its inclusion. Asimov delivered the final chapters to Basic Books on 21 April, and the appendices on 4 May.
When he began proofing the book's galleys, Asimov was horrified to find that Svirsky still cut out some 30% of the book's material. Asimov reinserted as much information into the galley proofs as he could, but he remained unhappy with the book.