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This expansive square, named after Christopher Columbus, commemorates the discovery of the New World. The three monumental slabs near Calle de Serrano were designed by Joaquín Vaquero Turcíos to symbolize the three ships that made the voyage to America in 1492. In the centre of the square is a more conventional sculpture of Columbus, erected in the 19th century. Note a relief on the base which shows Queen Isabel of Castile selling her jewellery to finance his enterprise.

This historic square off Calle Mayor has been the centre of local government since medieval times. Opposite the Casa de la Villa, is the Casa y Torre de los Lujanes, Madrid’s oldest civil building (15th-century). In the centre of the square is a statue of Alvaro de Bazán, the Spanish admiral who defeated the Turks at Lepanto in 1571 (see Golden Age). Erected in the late 19th century, it is by sculptor Mariano Benlliure. The palace on the south side is the Casa de Cisneros (1537), built for one of Spain’s most powerful families.

The streets around this well-known square boast the greatest concentration of tapas bars in the city and it’s often still buzzing at 4am. A plaque outside Hotel Reina Victoria honours the great bullfighter, Manolete, a regular guest until he was killed in the ring in 1947.

The look of this busy square reflects the sleek modernist architecture of 1930s America. Good examples are the curved Art Deco façade of the Carrión building (No. 3), the Palacio de la Prensa (No. 4) and the Palacio de la Música (Gran Vía 35), all now cinemas. Madrid is one of only a handful of cities in the world where you can still see hand-painted film posters.

This square in the heart of Malasaña commemorates the leaders of the insurrection of May 1808, Luis Daoíz and Pedro Velarde, who are buried in the Plaza de Lealtad. The site was chosen because, in those days, this was the artillery barracks of the Monteleón Palace, the main focus of resistance to the French. The brick arch now sheltering a sculpture of the two heroes was the entrance to the building. In the 1990s the square was taken over by under-age drinkers who gathered here at weekends for binges known as botellón . Though it has now been reclaimed by local residents, it is best avoided at night.

Ten streets radiate from this elliptical square, which for most madrileños is the real heart of the city. The name means “Gateway of the Sun” although the actual gateway was demolished in 1570. Of numerous historic events to take place here, the most dramatic occurred during the 1808 insurrection when snipers fired on one of Napoleon’s soldiers, provoking a massacre. Dominating the south side of the square is the 18th-century Casa de Correos, a post office which later became the Ministry of the Interior and the headquarters of General Franco’s secret police. A marker in front of the building indicates “kilómetro cero” , from which all distances in Spain are calculated. In the centre of the square is a statue of Carlos III and, on the corner of Calle del Carmen, a bronze statue of a bear climbing an arbutus tree, the symbol of the city.

Founded in the 18th century, the palatial premises of the Academy of Fine Arts house a collection of paintings surpassed only by the Prado and the Thyssen Bornemisza. Outstanding among the Spanish paintings are the Goyas, including the classic fiesta scene Burial of the Sardine . The academy also has an impressive array of works by European masters including Bellini, Tintoretto, Van Dyck, Rubens and Titian. Picasso and Dalí studied here for a time.