How does Mark Twain address the themes of slavery, freedom, and growing up in The Adventures of Huckleberry Finn?

These are some of the main themes of the novel. I will give you a brief explanation of each.

Freedom

Although often considered one of the first works of literary realism, there are also strong romantic themes in this novel. Huck's escape from the attempts to "sivilize" him in order to live freely on the river show his strong love of freedom. He can live according to his own passions rather than the forces of society. These romantic forces are an appeal to Emersonian individualism and freedom. The novel values the freedoms of the individual over the often corrupting forces of the society. This is also clear from Huck's desire to escape his father, as well as Jim's struggle to escape slavery.

Growing up

While this is an adventure novel, it is also in many ways a coming of age novel. In the previous book in the story, Huck is more of a follower than a leader. He goes along with Tom's plans like we see him do in the start of the book. Later, he reluctantly obeys social forces, then tags along with the King and Duke's schemes. 

Huck slowly grows out of his complacency and acts on his own. He breaks from moral convention by remaining loyal to Jim, and turns on the King and the Duke. He slowly becomes his own man. By the end of the novel, Tom's plans seem entirely ridiculous. Huck has outgrown the need to seek adventure for its own sake. The reader sees how silly such adventures were as Tom gets shot executing a plan that was pointless. Huck moves from being a young boy looking for fun to a man seeking the freedom to live according to his own values.

Slavery

This theme is explored through Jim's character. Jim is a close friend of Huck's. He is in many ways something of a father figure to the boy. Having grown up in an flawed society, Huck believes that allowing Jim to remain free is a sin. He grapples with this, since he has been convinced that alerting Jim's owner is the moral thing to do. His internal morality, however, says differently. He knows deep down that Jim is a good man and that slavery is wrong. His decision to "go to hell," and tear up the letter, shows how basic human goodness prevails over societal ideas of morality.