The last and perhaps the most complicated of the Abscam bribery trials is scheduled to begin in a federal courtroom in Brooklyn Monday, when Sen. Harrison A. Williams Jr. (D-N.J.) faces charges that he sold his office to undercover FBI agents in return for future profits from a titanium mine.

Unlike the previous Abscam trials, which have resulted in the conviction of six House members, there is no allegation that Williams accepted money from the undercover agents, who posed as representatives of Arab sheiks and recorded their transactions on videotape.

The indictment says instead that Williams, the third member of the Senate in 40 years to face criminal charges, agreed to seek government contracts to benefit a titanium mine in Virginia if the "sheik" would lend some friends $100 million. A second bribery count alleges that the senator later agreed to share in profits from a planned sale of the mine.

Alexander Feinberg of Cherry Hills, N.J., Williams' longtime attorney, is a co-defendant.

Williams, who was the powerful chairman of the Senate Labor and Human Resources Committee until the Republicans took control of the Senate this year, has denied the charges.

And he and his attorney, George J. Koelzer, have found help from an unexpected source: government attorneys who felt that undercover informer Melvin Weinberg violated Williams' constitutional rights by urging him to boast of his influence at a meeting with the "sheik" in June 1979.

Edward J. Plaza and Robert A. Weir, assistant U.S. attorneys in New Jersey, warned Weinberg later about his coaching tactics, but he replied: "If I don't put words into people's mouths we won't make no cases."

The conduct of Weinberg and two unwitting middlemen who introduced congressmen to the undercover agents has been the most controversial element of the Abscam investigation. At one point in the Williams investigation, Weinberg and middleman Angelo Errichetti reportedly forged a letter.

A federal judge in Philadelphia threw out the convictions of two city councilmen convicted of Abscam charges because he said the government created the crime and then entrapped the targets.

Though the Williams case wasn't before him, U.S. District Court Judge John Fullam went out of his way to attack the government's treatment of the senator. He said Williams was seeking financing for a legitimate business deal.

"Throughout the preliminary discussions, Sen. Williams made it very clear that the venture would not be dealing with the United States government, and that he neither could nor would be in any way involved with government contracts," Fullam wrote. He added that Williams "repeatedly rebuffed" suggestions on how to evade taxes on profits from resale of the mine.

Though defense attorney Koelzer can't use Fullam's opinion as evidence, he no doubt will try to make the same points during the trial. He also is expected to call Plaza and Weir as witnesses to attack Weinberg's conduct.

In pre-trial motions, Koelzer also attacked the motives of chief Abscam prosecutor Thomas Puccio, after reports that he was planning to write a book with a friend, Jack Newfield, a Village Voice columnist.

But trial judge George C. Pratt ruled late last week that Puccio had made no such agreement and could lead the government case. He also rejected several Koelzer motions to have a pre-trial hearing on the government's conduct in the case.

A key government witness is expected to be Henry A. (Sandy) Williams III, a New Jersey businessman who was named a co-conspirator in the indictment but agreed to testify against his friend, Sen. Williams. They are not related.