After a week devoted to choosing a jury and almost a week of pretrial motions, Theodore Robert Bundy, 32, went on trial here today on charges of first-degree murder, attempted first-degree murder and burglary.

Bundy, a former law student at the University of Utah, is accused of entering the Chi Omega sorority house at Florida State University in Tallahassee early on Jan. 15, 1978, and killing two women as they slept, then beating two others with a club. He also is charged with breaking into a nearby apartmet half an hour later and beating another woman.

The victims were Lisa Levy, 20, and Margaret Bowman, 21, both of St. Petersburg.

Photographs of bite marks on Levy's body are expected to play an important role in the state's case against Bundy. A forensic odontologist testified in pretrial hearings that the marks could have made by no one buy Bundy.

In his opening argument, defense attorney Robert Haggard said he would prove that at least four other sets of teeth could have made the marks.

But he directed most of his argument at the eyewitness identification of Bundy made by former sorority member Nita Neary in pretrial proceedings.

Neary said she saw Bundy at the sorority's front door on the morning in question and that he had a stocking-wrapped club in his hand. At the time, she gave police a description of the man, and she later identified Bundy in a police lineup. In pretrial proceedings, she again identified him as the man she had seen and said she felt "more certain than I ever have before."

Haggard spent most of his 30 minutes of argument calling attention to potential weaknesses in Neary's testimony.

Another key part of the state's case became evident today when prosecutors disclosed that a pantyhose mask found near one of the Tallahassee victims contained a hair similar to those of Bundy.

Prosecutor Dan McKeever said the mask was found on the floor of the duplex where Cheryl Thomas, also an FSU student, was beaten.

Sentenced to serve one to 15 years for a 1974 kidnapping in Utah, Bundy was extradicted to Colorado to stand trial for first-degree murder in the slaying o Caryn Campbell, 23, at a ski resort in January 1975. He escaped from jail before the trial.

Bundy faces a first-degree murder charge in the kidnap-slaying of Kimberly Diane Leach, 12, in Lake City, Fla., on Feb. 9, 1978.

Bundy is wanted for questioning in 36 other killings and disappearances, mostly in Utah, Washington and Colorado. He denies any involvement in the Chi Omega killings and the Leach case.

Bundy has taken charge of his defense. He often argues motions in court and sounds much like the lawyer he once hoped to be.

Bundy won a legal poitn when Circuit Court Judge Edward Cowart said today that the jury would not be told that the defendant allegedly once said that he felt " like a vampire" and that he feared that uncontrollable fantasies were taking over his life.

The comments allegedly were made in a conversation Bundy had with police the day after his capture in Pensacola. Cowart said he was concerned about testimony that a prosecutor had kept Bundy from consulting with public defenders during the night. Police say Bundy waived his rights to consult a lawyer.

The jury was kept out of the court while attorneys argued over what the panel could hear.

The judge also refused to bar television coverage of the trial, rejected a request that the trial be delayed so the defense attorneys could het some sleop, and told a complaining defense lawyer that she would grow accustomed to the long court hours. CAPTION: Picture, THEODORE ROBERT BUNDY . . . argues his own motions