Madrid's shopping splits between three distinct zones. The grand bourgeois shopping district is the Salamanca neighbourhood, with the international luxury brands lining Calle Serrano and the side streets — Loewe, Hermès, the Spanish jewellers Suarez, and the Madrid flagships of every major European fashion house. The grand-old-Spain department store El Corte Inglés has half a dozen branches around the city; the flagship is on Calle Preciados just off Puerta del Sol.
For something more characterful, the El Rastro flea market every Sunday morning in La Latina is the great Madrid shopping experience — antique books, vinyl, vintage clothing, hardware, and a fair amount of junk spread across a maze of streets south of Plaza de Cascorro. The Mercado de San Miguel by Plaza Mayor is restored, beautiful, and aimed at tourists; the neighbourhood markets of San Antón in Chueca and Antón Martín in Lavapiés are cheaper and more local.
For specialty: Casa de Diego (fans) at Puerta del Sol since 1858, Antigua Casa Talavera (ceramics from across Spain) on Calle Isabel La Católica, El Flamenco Vive for flamenco gear, and the Sunday morning stamp and coin market in Plaza Mayor.