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Mr. Musk sued OpenAI in 2024, claiming that the nonprofit he funded with his own large donations took advantage of his financial resources. He also argued that OpenAI breached its founding agreement by putting commercial interests over the public good.

Mr. Musk is asking for more than $150 billion in damages from OpenAI and Microsoft, OpenAI’s primary partner. He is also asking the court to remove Mr. Altman from the start-up’s board and stop a shift the company recently made to operate as a for-profit company.

OpenAI and Mr. Altman deny Mr. Musk’s claims that they abandoned the nonprofit’s mission. They have filed court documents that show Mr. Musk also tried to shift the start-up toward commercial purposes before his exit.

The trial’s outcome could upend the A.I. landscape. OpenAI, which has emerged as one of the most important tech companies in the world, could be hobbled just as it appears to be heading toward one of the biggest initial public offerings in history. A win for Mr. Musk, who has his own for-profit lab, xAI, would also be a win for OpenAI’s competitors, from industry giants like Google to young companies like Anthropic, as well as international competitors such as China’s DeepSeek.

If Mr. Musk loses, Mr. Altman will likely solidify control of a company that has become synonymous with corporate dysfunction. And OpenAI, which is now valued at about $730 billion, will be free to pursue a data center expansion plan that could cost hundreds of billions of dollars.

(The New York Times has sued OpenAI and Microsoft, claiming copyright infringement of news content related to A.I. systems. The two companies have denied the suit’s claims.)

Here’s what to know:

• High-profile witnesses: Mr. Musk, Mr. Altman and several other key industry figures, including Microsoft’s chief executive, Satya Nadella, and Mira Murati, OpenAI’s former chief technology officer, are slated to testify in the trial.

• Trial logistics: The trial is set to run for about four weeks before a nine-person jury at the federal courthouse in Oakland, Calif. If the jury rules in Mr. Musk’s favor, Judge Yvonne Gonzalez Rogers — who also oversaw a high-profile lawsuit against Apple over its control of the App Store — will decide on monetary damages and other remedies.

• What’s at stake: Mr. Musk’s suit demands more than $150 billion in damages from OpenAI and Microsoft. In a recent court filing, he amended his complaint to ask that these damages be shared with the OpenAI nonprofit. He also seeks to remove Mr. Altman from the OpenAI board of directors and unwind the shift that OpenAI recently made to a more traditional for-profit company.

Satya Nadella, Microsoft’s chief executive, is expected to testify. Shivon Zilis, a former OpenAI board member and the mother of at least four of Mr. Musk’s children, is on the witness list. So is Tasha McCauley, another former OpenAI board member, who tried to fire Mr. Altman.

That Oakland is playing host to this tech industry pantheon is one of the many oddities in this high-stakes trial. While plenty of tech workers live in Oakland, only a handful of tech companies are based in “The Town,” as locals call it. The go-go tech culture of San Francisco and Silicon Valley is notably absent in this city, even though it is only about 12 miles from OpenAI’s headquarters.

“Oakland is an interesting city for this to happen in, because we’re kind of thought of as the other town,” said Lesley Mandros Bell, an artist and teacher who has lived in Oakland for nearly four decades.

The Oakland federal courthouse is part of a soaring, postmodern complex built in 1993 and named for Ronald Dellums, a longtime congressman whose district included Oakland and who served as the city’s mayor from 2007 to 2011. But Mr. Dellums, who died in 2018, might have frowned upon the ruthless capitalism that will be on display in the building named after him. He was a democratic socialist whose politics landed him on President Richard M. Nixon’s “enemies list.”

“We start with a humanistic value system and ask: What inhibits life and growth?” Mr. Dellums said in an interview in 1976. “The answer is war, pollution, elitism, corporate corruption, corporate power that controls over 90 percent of the wealth and dominates people’s lives.”

When Mr. Musk founded OpenAI with Mr. Altman and several young A.I. researchers, he saw the research lab as a necessary counterweight to the A.I. work underway at Google. He believed that Google and Larry Page, one of its founders, did not understand the dangers of A.I.

OpenAI’s founders — backed largely by donations from Mr. Musk — vowed to freely share their technology with the public as open source software. They argued that A.I. would be too powerful and too dangerous to be controlled by a single company.

But by late 2017, many inside OpenAI were arguing that open sourcing may be more dangerous than keeping the technology closed. And they worried that if the lab remained a nonprofit, it might not raise the money needed to reach its lofty goal of building artificial general intelligence, or A.G.I., a machine that can do anything the human brain can do.

That included Mr. Musk. In February 2018, he forwarded an email to the lab’s other founders suggesting that OpenAI attach itself to Tesla, his electric car company, and build its A.I. using the supercomputers that Tesla was developing.

“Tesla is the only path that could even hope to hold a candle to Google,” he wrote. “Even then, the probability of being a counterweight to Google is small. It just isn’t zero.”

After Mr. Altman and others refused to give Mr. Musk control, he quit. Later that month, he announced his departure to OpenAI’s staff on the top floor of the lab’s office in San Francisco. He withdrew his financial support for the lab.

Forced to find other sources of funding, Mr. Altman bolted a for-profit company onto the original nonprofit and eventually raised $13 billion from Microsoft. The lab also curtailed its efforts to open-source its technologies.

OpenAI has since emerged as one of the most important tech companies in the world, worth an estimated $730 billion as a for-profit company overseen by the original nonprofit. The start-up is heading toward one of the biggest initial public offerings in history, which could come as soon as this year.

The company has expanded to more than 4,000 employees working in offices around the world, and is pursuing a data center expansion plan that could cost hundreds of billions of dollars.