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The focal point of this beautiful square is the bronze equestrian statue of Felipe IV, moved here from the Buen Retiro palace in 1842. The sculptor Pietro Tacca took advice from Galileo on the modelling of the rearing horse – the figure of the king was based on sketches by Velázquez. The statues of Spanish rulers were intended for the balustrade of the Palacio Real but they did not meet with royal approval.

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.

On 2 May 1976 a young couple climbed on to the statue of Daoíz and Velarde and performed a striptease in front of a boisterous crowd of youngsters celebrating on the square. This was one of the first manifestations of the movida (scene), a period of hedonism, enthusiasm and creative energy

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.

In 1919 Alfonso XIII opened Madrid’s first metro line and the city was – literally – on the move again, after decades of inertia. Whole streets were demolished to make way for the Gran Vía’s bars and restaurants and Calle de Alcalá became the heart of a new financial district.

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.