FBI trainee Clarice Starling is pulled from her training at the FBI Academy at Quantico, Virginia by Jack Crawford of the Bureau's Behavioral Science Unit. He assigns her to interview Hannibal Lecter, a former psychiatrist and incarcerated cannibalistic serial killer, whose insight might prove useful in the pursuit of a serial killer nicknamed "Buffalo Bill", who skins his female victims' corpses.
Starling travels to the Baltimore State Hospital for the Criminally Insane, where she is led by Frederick Chilton to Lecter's solitary quarters. Although initially pleasant and courteous, Lecter grows impatient with Starling's attempts at "dissecting" him and rebuffs her. As she is leaving, one of the prisoners flicks semen at her. Lecter, who considers this act "unspeakably ugly", calls Starling back and tells her to seek out an old patient of his. This leads her to a storage shed where she discovers a man's severed head with a sphinx moth lodged in its throat. She returns to Lecter, who tells her that the man is linked to Buffalo Bill. He offers to profile Buffalo Bill on the condition that he be transferred away from Chilton, whom he detests.
Buffalo Bill abducts a U.S. Senator's daughter, Catherine Martin. Crawford authorizes Starling to offer Lecter a fake deal promising a prison transfer if he provides information that helps them find Buffalo Bill and rescue Catherine. Instead, Lecter demands a quid pro quo from Starling, offering clues about Buffalo Bill in exchange for personal information. Starling tells Lecter about the murder of her father when she was ten years old. Chilton secretly records the conversation and reveals Starling's deceit before offering Lecter a deal of Chilton's own making. Lecter agrees and is flown to Memphis, Tennessee, where he verbally torments Senator Ruth Martin and gives her misleading information on Buffalo Bill, including the name "Louis Friend".
Starling notices that "Louis Friend" is an anagram of "iron sulfide"Â â fool's gold. She visits Lecter, who is now being held in a cage-like cell in a Tennessee courthouse, and asks for the truth. Lecter tells her that all the information she needs is contained in the case file. Rather than give her the real name, he insists that they continue their quid pro quo and she recounts a traumatic childhood incident where she was awakened by the sound of spring lambs being slaughtered on a relative's farm in Montana. Starling admits that she still sometimes wakes thinking she can hear lambs screaming, and Lecter speculates that she is motivated to save Catherine in the hope that it will end the nightmares. Lecter gives her back the case files on Buffalo Bill after their conversation is interrupted by Chilton and the police, who escort her from the building. Later that evening, Lecter kills his guards, escapes from his cell and disappears.
Starling analyzes Lecter's annotations to the case files and realizes that Buffalo Bill knew his first victim personally. Starling travels to the victim's hometown and discovers that Buffalo Bill was a tailor, with dresses and dress patterns identical to the patches of skin removed from each of his victims. She telephones Crawford to inform him that Buffalo Bill is trying to fashion a "woman suit" of real skin, but Crawford is already en route to make an arrest, having cross-referenced Lecter's notes with hospital archives and finding a man named Jame Gumb, who once applied unsuccessfully for a sex-change operation. Starling continues interviewing friends of Buffalo Bill's first victim in Ohio while Crawford leads an F.B.I. tactical team to Gumb's address in Illinois. The house in Illinois is empty, and Starling is led to the house of "Jack Gordon", who she realizes is actually Jame Gumb, again by finding a sphinx moth. She pursues him into his multi-room basement, where she discovers that Catherine is still alive, but trapped in a dry well. After turning off the basement lights, Gumb stalks Starling in the dark with night-vision goggles, but gives his position away when he cocks his revolver. Starling reacts just in time and fires all of her rounds at Gumb, killing him.
Some time later, at her FBI Academy graduation party, Starling receives a phone call from Lecter, who is at an airport in Bimini. He assures her that he does not plan to pursue her and asks her to return the favor, which she says she cannot do. Lecter then hangs up the phone, saying that he is "having an old friend for dinner", and starts following a newly arrived Chilton before disappearing into the crowd.

Question: Why does the FBI want to interview Hannibal Lecter?
Answer: To gain insight into tracking down a new serial killer.
Alternative answer: For his insight into the murderer