In My Antonia, how does the relationship between Jim and Ántonia evolve?

The nature of the relationship between Jim and Antonia reflects idealism and transcendence can exist in the interactions between human beings.  While time changes both Jim and Antonia, there is something profound about the connection between both.  Since Jim's coming of age is the focus of the narrative, the reader understands that Jim's connection to Antonia is something that changes over time, yet remains strong and intact as an indelible part of his identity.  While Antonia lives her own life, the distinct reality which emerges is that the beauty and passion that she exhibited towards life and Jim will never leave.  As time passes, the relationship between both acquires greater intensity and depth precisely because time has formed both of their identities.  In the end, the relationship between both speak to the transformation from the specific to the universal.

One way in which Jim and Antonia form a special connection is through their shared sense of Romanticism and what it means to dream.  Jim is fascinated with the idea of the "shapeless" nature of the nation.  His foray into the Plains is one where the immensity of this condition strikes him.  He is able to channel his Romanticism into his affections for Antonia.  Like the shapeless world around him, Antonia is a force that is able to give form to that which lacks it. Over time, the connection between both of them takes on different forms. As with the promises and possibilities of the land that has captured Jim's imagination, Antonia comes to represent much in way of what can be, as opposed to what simply is: "I'd have liked to have you for a sweetheart, or a wife, or my mother or my sister – anything that a woman can be to a man." The nature of the relationship between both of them contains the capacity to dream and to hope.  It is one that transcends daily life and moves into the realm of what can be as opposed to being tethered to what is. Antonia has imprinted herself onto Jim:  "The idea of you is a part of my mind...You influence my likes and dislikes, all my tastes, hundreds of times when I don't realize it. You really are a part of me."  For her part, Antonia's sense of imagination is large enough to encompass Jim, but also envision what her life can be.  In this regard, the relationship that both share is reflective of the capacity to dream and to transform what is into what can be. 

As the novel progresses, it becomes clear that the idea of transcendence fits into how Jim and Antonia view one another.  The world in which they inhabit seems too small for their dreams and sense of imagination.  Jim experiences this when he recognizes that even sex and carnal contact is secondary to the transcendent nature in what Antonia represents:  "I used to wish I could have dreams like this [of a sexual nature] about Antonia, but I never did."  Lena represents the sexual outlet of Jim's base nature, a statement of what is. However, Antonia captures his transcendent imagination. This is a reflection of how their relationship is more than what is around them.  Cather deliberately leaves it ambiguous as to what that relationship exactly is.  Part of the reason for this is because dreams are never easy to quantify.  They exist in a realm devoid of specificity and their beauty is their elusiveness and transcendence. This is the condition that Jim and Antonia occupy to one another, something that becomes evident in his mind at the end of the novel:

She lent herself to immemorial human attitudes which we recognize by instinct as universal and true. I had not been mistaken. She was a battered woman now, not a lovely girl; but she still had that something which fires the imagination, could still stop one's breath for a moment by a look or gesture that somehow revealed the meaning in common things. She had only to stand in the orchard, to put her hand on a little crab tree and look up at the apples, to make you feel the goodness of planting and tending and harvesting at last. All the strong things of her heart came out in her body, that had been so tireless in serving generous emotions.  It was no wonder that her sons stood tall and straight. She was a rich mine of life, like the founders of early races. 

Jim's understanding of Antonia and what she means has changed as time has passed. It has superseded time. Antonia might have physically changed, but the spirit of beauty that is in her has never left.  The transformative condition of her being that meant so much for Jim has come to mean even more as time has passed. For Jim, Antonia represents an ideal, a real in which "strong things" emerge.  She comes to represent an almost divine emanation that connects to the past, "like the founders of early races."  For her part, Antonia is able to recognize that her gift lies in her ability to find happiness in this life.  She embraces her dreams because they are a reflection of this passion for living. Jim is a part of that.  Antonia is symbolic of a zeal in consciousness, represented "in the full vigor of her personality, battered but not diminished." This is represented by what she feels for Jim, but is also beyond him.  It is a spirit of life that is larger than simply him.  As with Jim's view of her, Antonia's view of him is larger than specificity.  It is a condition of being in which the individual embraces a transcendent view of consciousness, one that transforms the people around them as reflective of a universal energy as opposed to a specific persona.  As time has passed, Cather suggests that their relationship has transcended the banal labels that human beings use.  It has transformed into something more universal that they don't singularly possess, but rather share between them.

In "My Antonia", who learns more through their relationship, Jim or Antonia?

You will probably get some differing viewpoints on this from many teachers, but I believe Jim learns more.

First of all, Jim is the narrator, so we are privy to his innermost thoughts. The story of Antonia is only told through Jim's narrative, and Jim's perspective, so we truly don't know what she learns, just what Jim thinks she may have learned.

Also, from the beginning, Jim is a brooding, alienated (orphaned), cerbral character. He learns a lot about who he is and who he is not from observing the way Antonia lives, the way she interacts with her family and others (not always to her betterman), and by weighing his own philosophies and way of life against hers, he learns more about himself. We don't have any evidence in the novel that Antonia does this in return. In fact, she mostly rejects the way Jim chooses to do things and when he gives her advice about some of the mistakes he thinks she is making, she ignores it.

Finally, at the end of the novel, it is Jim who returns to Nebraska seeking out some solace after his failed marriage. He is a successful attorney, but his life is empty and lonely. He admires what Antonia has, a loving husband, a big family, and he again compares his life to hers and finds his lacking.

Jim is Willa Cather's "voice" as well as a character, therefore his lessons, I believe, are the more prominent ones.