The sari, the Nehru jacket, the cotton prints known as Indiennes, the paisley shawls and rich embroideries. India’s silhouettes, fabrics, and design techniques—refined and exported over centuries—have inspired fashion in the ateliers of the haute couture and in the street. Forty garments and more than 20 accessories, from the 19th to 21st centures, showcase the historic and exuberant influence of India. —L.J.