A six-year dispute between Oracle Corp. and Alphabet Inc. ’s Google over software copyrights heads back to court Monday for a trial that could lead to billions of dollars in damages and alter the ground rules for modern software.

It will be the second trial for Oracle’s complaint that Google used parts of its Java software without permission. In 2012, a jury found Google infringed Oracle’s copyrights, but the judge later ruled the software couldn’t be copyrighted. Since then, the case has ping-ponged through appeals courts, including a brief stop at the U.S. Supreme Court.

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Mark Lemley, a Stanford University law professor who has tracked the case, said a victory for Oracle could deter programmers from using APIs to make apps and websites more useful.

“It could stifle programming innovation, especially among small, independent programmers” who can’t afford to pay licensing fees, said Mr. Lemley, who worked as an outside attorney for Google several years ago in a separate case.