The enotes Study Guide on Coelho's The Alchemist lists the following themes for the novel. I'll add a brief explanation for each.
- magical realism: not just as a literary technique, but as a way of existence. The universe conspires to help one succeed.
- numerology: there are four elements, four obstacles in Santiago's way, three coins, three characters speak to each other in the caravan, etc.
- patience: Santiago learns it as a shepherd, in the merchant's shop. One must not hurry or one might miss omens or signs.
- perception: Santiago fears gypsies because of what he's heard, and accepts the robber boy because he wants to.
- religion/spirituality: parallels to the Bible abound: Jesus, Joseph, Melchizedek, who even appears.
- water: it can be either a positive or negative force; tears represent what one must endure.
In case you're not familiar with magic realism, the world presented is a realistic world in which the supernatural exists. That may seem like a contradiction, but all it means is that supernatural events are included in a story that is otherwise realistic. This is different, say, from a fantasy world such as Harry Potter's, or a science fiction world such as that in Star Wars.