What significant themes does the Alchemist present?

I would say that a major theme that runs throughout the story is a theme about personal hopes, dreams, and fulfillment. Santiago is on a search for treasure and his own Personal Legend. Along the way, he meets with adversity. Whether it's desert bandits or something else, obstacles are constantly thrown in his path. Santiago is constantly impeded from obtaining his goal, yet the goal is important enough to never give up. This is also another theme of the novel. There is a theme of perseverance and patience. Santiago doesn't immediately get what he is searching for.  It takes him time to achieve his goal, and that sends a powerful message to readers. Good things can come to people who are patient and willing to work for it.  
Finally, it would be remiss to not mention the theme that's in the novel about spirituality and the natural world. Santiago is not just on a journey for wealth. He's also searching for a pure soul. In order to achieve his Personal Legend, Santiago must learn to tap into the Soul of the World. Once he is able to do this, he learns that all of creation is different forms of the same spirit.