Don Quixote believes that the windmills really were giants—but that they were turned into windmills by his nemesis, a magician named Friston.
The windmills that Don Quixote spots in the distance are always windmills; they're never giants. But Don Quixote is so convinced that they're windmills that he attacks them. Doing so breaks his lance and throws both him and his horse into the air.
After he's helped up by Sancho Panza, he has to explain why the giants are gone and only windmills are in their place. Instead of recognizing that he's made a mistake, Don Quixote insists that the windmills were once giants. He says that Friston—the same person he thinks stole his books—turned them into windmills. Don Quixote says that the magician did so to deprive Don Quixote of the honor of slaying the giants.
Sancho Panza recognizes from the beginning that the things in the distance are windmills.
Don Quixote battles the windmills because he believes that they are ferocious giants. He thinks that after defeating them -- all "thirty or forty" of them! -- he will be able to collect the spoils and the glory as a knight. However, when he charges the "giants," his lance gets caught in a sail. The lance snaps and Don Quixote and his horse Rocinante are hurled some distance away to the ground.
When Sancho Panza asks Don Quixote what happened, Don Quixote laments that his enemy, the evil necromancer who stole all of his books, has also turned the giants into windmills at the last second. He did this to humiliate Don Quixote and steal Don Quixote's chance to fight in a glorious battle.
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