It took the neighbors a long time to warm up to Modernisme. When Gaudí’s last secular commission, Casa Milà, was finished in 1912, they took one look at the undulating lines of seemingly wind-eroded rock and dubbed the building La Pedrera (“the stone quarry”). The shock of its novelty has faded, but the nickname has stuck as a term of endearment. With a sinuous, rippling facade, it is one of the most beloved of Gaudí’s works (and another spot where purchasing an advance ticket online will save you precious time as well as several euros). The tour includes the patios and the Espai Gaudí, a handsome maze under the roof rafters with engineering and architectural didactics that help you to get into Gaudí’s mind. (He calculated, for instance, the loads an arch could bear by hanging weights on knotted cord to get the shapes he wanted, then extrapolating to life size.) The Pedrera Apartment evokes an era when the elegant apartment house was new, complete with Gaudí furniture. Substitute a modern music system for the Edison phonograph, and most visitors would be ready to sign a lease on the spot. Gaudí saved his grandest gestures for the rooftop, transforming functional chimneys into a sculpture garden of swirling mosaic forms and ominous hooded warriors. Gaudí intended the roof as an open-air terrace, and during the summer, jazz musicians hold forth several evenings each week. Amid the chimneys Gaudí built a lovely parabolic arch to frame the towering steeples of his masterpiece, La Sagrada Familia; if you are patient long enough for the crowds to part, it’s the classic Barcelona selfie. For a more intimate (and more expensive) nighttime visit, choose the “Origins” tour, which includes a glass of cava on the rooftop.