Third Person (Omniscient)
Throughout this book, Cervantes uses multiple layers of narrators. For starters, there's Cervantes himself, who speaks to us in his Author's Prefaces that begin Parts 1 and 2 of the book. Further, Cervantes also takes on the role of narrator for Book 1 of Part 1. At the end of this Book, he passes the role of narrator on to "the second undertaker of this work" (18.104.22.168). From that point onward, the telling of the story is given to a Moorish (African) historian named Cid Hamet Benengeli.
Playing on the racist stereotypes of his time, Cervantes chooses an African historian as his new narrator in order to inject suspense and doubt into everything that happens in his book, claiming that "I must only acquaint the reader, that if any objection is to be made as to the veracity of this, it is only that the author is an Arabian, and those of that country are not a little addicted to lying" (22.214.171.124).
But for all of his changes in narrator, Cervantes's story always remains Third Person Omniscient. It is not Third Person Participant because neither Cervantes nor his fictional historian ever show up in the actual story of Don Quixote's adventures. It's not Third Person Limited, either, because we have access to the thoughts of all characters, not just Don Quixote, as you can see with a line about a secondary character like the Duchess that tells us: "The Duchess was ready to die with laughter at Sancho, whom she thought a more pleasant fool, and a greater madman than his master" (126.96.36.199).
Here, we get to see directly what the Duchess is thinking; we wouldn't be able to see that if the narrator were Third Person Limited, giving us access only to Don Quixote's thoughts.
The use of Third Person Omniscient is suitable for this book: there are so many characters who try to manipulate Don Quixote and Sancho, and it would be tough to follow their plans if we could only see what was happening from Don Quixote's perspective.