What are your opinions about the relationship between Agent Starling and Dr Hannibal Lecter?

I think he saw her as something of a 'naive stray' when they first meet.
A feeble attempt by either Chilton or Crawford to see if she could somehow entice him into revealing details about either 'Buffalo Bill' or indeed his own crimes.
("I'm not sure who is the greater fool"

I think he says as much when reading the questionaire she gave him.

But i think she surprised him with the answers to the questions he asked her. Her honesty and plain speaking (The 'truth about Multiple-Miggs' etc.) were probably something he hadn't heard anyone say to him in a long time.
So i guess he has to re-adjust his thinking toward her.

When he asked her about how she felt when she found Benjamin Raspail (or his head at least)in the rear of the funeral car in the storage lock-up.) She was honest again and that i think kinda surprised him.

So there are all these incidents which probably see his view of her evolve from scared newbie to serious and resolute 'equal' to someone to be admired.

But ultimately I think he sees her as someone who he would have taken care of in another life.
Kinda 'Father-Daughter'.

Dr Lecter was a super hero. He only ate people who deserved it. Starling is a good person, so she has nothing to fear from him. He would have eaten Buffalo Bob if he had the opportunity.

He sees the darkness in her.

Starling was a pawn in Lecter's grand master chess game.

didn't read the book but I suspect she was falling under his spell

she tried to be in charge - but he clearly had her

and when he got her to expose herself vulnerabilities I swear he climaxed

She was gagging for a go on his todger