Miss Brennan's disclosures about Jobs's behaviour could reignite a simmering dispute with his family. Her invitation to Jobs' memorial service at Stanford University was withdrawn after she co-operated with Rolling Stone magazine on an article about their relationship.
The book, subtitled A Memoir of My Life with Steve Jobs, has returned the late Apple chief to the pages of America's tabloids with extracts published in the New York Post.
According to Miss Brennan, a painter and graphic designer who lives in Monterey, California, Jobs was a "brilliant misfit", convinced he was going to die young, who became "positively despotic" over time. "As Apple grew, so did Steve's sense of self-entitlement," she writes.
A cute tale he would later tell, about colleagues at Atari computers in the early 1970s not wanting to work the same shift as him because he smelled bad, is untrue, Miss Brennan claims. In fact, "I had heard that he was moved to the night shift because his co-workers found him so dark and negative," she writes.
The couple met as pupils at Homestead High School in Cupertino, California, the city in the foothills of the Santa Cruz Mountains in which Apple's headquarters, at 1 Infinite Loop, remains today. They went on to live together as Jobs and a friend co-founded the firm from a garage.
However, he ended the five-year relationship just as the firm was taking off and when Miss Brennan became pregnant with their child. Jobs denied being the father of the couple's daughter, Lisa, for years after she was born in 1978. "Steve's face turned ugly," she said of the moment she told him she was pregnant. "He gave me a fiery look. Then he rushed out of the house without a word." The denials persisted for several years. Jobs at one point accused Miss Brennan of "stealing my genes", which he saw as a valuable commodity, and failed to visit for three days after she gave birth.
At the same time, he continued to aggressively dispute the notion that he was Lisa's father, even recruiting lawyers to draw up plans of Miss Brennan's house to show how other men might have been visiting her. Yet a DNA test proved Jobs wrong, prompting him to agree to pay about US$500 ($588) each month in child support, shortly before the flotation of Apple stock made him millions. Lawyers who then worked with Jobs at Apple later told Miss Brennan that he and his colleagues had celebrated extravagantly after he escaped having to pay more towards his daughter's upkeep.
Miss Brennan dates this hostile attitude towards women to a transformational trip that Jobs took in 1974 to India with Daniel Kottke, a friend and collaborator on the first Apple computer, after the 20- year-olds became captivated by the book Be Here Now by the American guru known as Ram Dass.
Before he died, Jobs said his work had been influenced deeply by his seeing how the people of the Indian countryside relied more on intuition than intellect. The formative trip is depicted in several key scenes of Jobs, the Hollywood biopic that was released this year.
The sojourn also helped him "see the craziness" of the Western world, and turned him on to Eastern mysticism, he later said. However, according to Miss Brennan, Jobs also returned from his visit a "bewildered lunatic shaman" and fully-fledged sexist bully.
Having come back covered in bed-bugs and full of parasites, Jobs declared to her that "if women were good, they wouldn't experience labour pain", and compared women to "a snake in the grass".
He also "started to reject the feminine aspect as inferior to the glorious masculine", and became markedly more sexually aggressive, his former girlfriend said.
"It all broke open between us when he asked if I would make tantric love with him in his garden shed," said Miss Brennan. She felt neither was spiritually prepared and "the only word I had was an emphatic 'no"'.
The couple "shared nights of lovemaking so profound that, astonishingly, some 15 years later, he called me out of the blue to thank me," she said. However, Jobs was so concerned about saving "energy for work" and "conserving one's vital energies" that he preferred not to climax.
Colleagues have recalled widely how Jobs drove staff at Apple into the ground with his exhausting demands, his refusal to compromise on his vision and his furious criticism of those he considered inferior or incompetent.
Despite Apple's rise, Jobs was fired from the empire he had founded at just 30, following a dispute with the company's chief executive amid poor sales of the Macintosh computer.
However, he never lost his distinctive drive and remarkable self-belief, and resumed his exacting leadership when he returned to a beleaguered Apple in 1997.
Jobs, who left a US$8 billion fortune, married Laurene Powell in 1991. They had three children.
