The Grand Trianon is a single-storey palace of pink and white marble, built by Louis XIV in 1687 at the far north end of the gardens as a private retreat from the ceremony and crowds of the main palace. It is about 2km from the palace entrance — far enough that only those who are serious about seeing everything make it here, which means it's usually far less crowded.
Louis XIV designed it as a place to escape the rigid protocol of court life, and the architecture reflects that: it is restrained by Versailles standards, horizontal and open, with a long arcade that looks out on the gardens. He used it as a place to meet his mistress Madame de Maintenon and later lived here more than in the main palace toward the end of his life.
Napoleon Bonaparte restored and refurnished it in the Empire style — much of what you see inside dates from his period of occupation. General de Gaulle later used it as a guest residence for visiting heads of state. The gardens around it are a quieter, more intimate version of the main gardens, worth exploring after the palace crowds.