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.
The primary theme in the alchemist is to follow ones dreams. Santiago has a dream and at first he is unsure to follow it. He is a Shepard boy who sells his sheep and goes on the journey.
Another theme is the that the journey itself is the gift of the dream. When Santiago embarks on his journey he is unaware what he will find. He has gone in search of a treasure that he has dreamt about. On the way he meets and experiences different things including the meeting of Fatima whom he falls in love with.
After he has made his journey he does not find the treasure but he learns that it was there all along. The journey had been the treasure and the experiences he had on the trip.