I never read "The Catcher in the Rye" but why would John Lennon's murderer shoot him multiple times and sit on the steps of the Dakota hotel near the scene of the crime and read this book while he waited for the cops to come.

Because he's a psychopath.

The book is about a lonely, clueless, angst ridden teenager.

According to Wikipedia,he wasn't reading it, the policeman at the scene said "(he) was holding a paperback book (J.D. Salinger's The Catcher in the Rye), and a cassette recorder, along with more than ten audio cassettes, with 14 hours of Beatles' songs on them.

He later apparently claimed the book The Catcher in the Rye would explain his perspective and motivation. A friend of Chapman recommended The Catcher in the Rye to Chapman, and the story took on great personal significance for him, to the extent that he reportedly wished to model his life after its protagonist, Holden Caulfield. In September 1980 he wrote a letter to a friend, Lynda Irish, saying "I'm going nuts", signed "The Catcher in the Rye"


For more info, see Wikipedia, and the reference sources:
http://en.wikipedia.org/wiki/Mark_David_Chapman
http://en.wikipedia.org/wiki/John_Lennon

Dang. The man had to be as crazy as all heck. Tell me, do you think that folks are right when they say that his warped mind told him to do it to make a name for himself If so, he needs to stay where he is.

In The Catcher in the Rye, the protagonist is a person who is a rebel, a misfit, and is mentally ill.

in "the catcher in the rye" holden first find profanity written on stairs in an elementary school thus shattering his innocent view on children. i'm not sure what that has to do with the murder but stairs were quite significant in the novel.

Well, that book is pretty depressing. It wouldn't surprise me if it's the reason behind even one murder. I was pretty angry myself after reading it. At least I didn't kill anyone, but I can understand why someone would after reading that. It's a terrible book. It can destroy someone.

The book is about hipocricy and phoniness of the world, and he could have seen John Lennon as hypocrite: he is a millionaire who sings about having no possessions.

probably an attempted suicide. i read the book i know. he probably tried to bore himself to death before the cops could take him to jail.