Jim presents a number of characteristics that seem to be in conflict with one another. He is bold enough and sly enough to run away and subtle on occasions as well. At the same time, he is gullible, foolish, superstitious and docile.
The contradictory nature of his character is also seen in his status as a "free slave". This is even true while he is on the run, as he is free as long as he is not caught - a contradiction in terms and in fact. The thematic notion of "contradiction" would be a good line to take for an essay, opening up an exploration of his character to its complexities in persona and legal/social status.
He has been recognized by critics as a complex character, at once a superstitious and ignorant minstrel-show stereotype but also an intelligent human being who conveys more depth than the narrator...
Jim displays his savvy when he finds Huck's father dead in a house floating down the river. He does not let on that the man he finds is Huck's father, sparing Huck from the news and the emotion that would surely come from it.
Alternatively, Jim's gullible nature is on display when Huck tricks him and lies to him with a number of childish ruses in the first half of the novel. Jim's superstitions are explored in this section of the novel as well.
Jim...can be seen as superstitious, ignorant, and servile "Uncle Tom" Negro. At the same time, Jim is one novel's most appealing adult characters in the book...
Above all, I see freedom as a primary theme in the book. Jim is a runaway slave; think about the freedom of drifting down a river on a raft, dropping a line in the water to catch a fish or just watching the shoreline. No parents, no "owners," no teachers, no proper citizens, no clergymen to judge one's actions.
A second theme is morality. Jim is a runaway slave and Huck, though Jim's friend and actually no smarter or better educated, no richer, etc., is white and entitled. Huck wrestles with the moral decision whether to turn his friend over to authorities or help Jim reach freedom, a return to the first theme.
Maturity is a third theme. Jim has time to think and he and Huck have time to mull over the inequalties of life. Jim begins to think on a broader, deeper level as he becomes more determined not to go back to his old life.
The influence of society is a theme. A young white man traveling with an older black male would draw the public's attention and questions about that relationship. You can see that Huck is uncomfortable at times being seen with Jim. Jim feels uncomfortable being seen with Huck. Friends, yes, but Jim will always be at a disadvantage in "polite" society.