How has Huck and Jim’s relationship changed since the beginning of the novel?

Huck's attitude towards Jim changes from him thinking that Jim is just property and an ignorant slave that is below him, to feeling that Jim is his good friend, and equal to him. Huck was raised in a society that devalued the individuality and humanity of slaves; slaves were property to be owned, who couldn't think for themselves, not actual humans with feelings and thoughts. Take for example the numerous pranks that Huck pulled on Jim--they reflect Huck's attitude towards Jim. After the incident where Jim and Huck get separated in the fog, Huck actually thinks that Jim is stupid enough to believe that none of it had happened, and that Jim had imagined it all. Jim calls him on this, chastising Huck for his lack of sensitivity. Huck says,

"It was fifteen minutes before I could work myself up to go and humble myself to a nigger."

This reflects his attitude of superiority over Jim. First of all, he obviously thinks Jim has no intelligence and can be had by a little kid's stupid prank, then he has a hard time "lowering" himself to apologize. Another telling incident is when they argue over language and King Solomon. They argue for a while, but then Huck gives up, stating,

"it warn't no use wasting words--you can't learn a nigger to argue. So I quit."

Here he reflects his attitude that Jim is incapable of learning, using reason and logic, or making intelligent arguments.

Later though, Huck's attitude changes. As Jim and Huck experience a lot of trials together, Huck learns to respect and care for Jim as a human being, and as an equal. At the end, he even goes so far as to say about Jim, "I know'd he was white inside." This statement shows how Huck feels that Jim is, to an extent, his equal. His attitude towards Jim has changed from him feeling Jim to be below him and less of a human, to being his equal.