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El Retiro Park
The main park of Madrid, the perfect place to take a rest during a sunny day, or take part in the drum circles around the statue of Alphonso XII on summer evenings. There is a large boating lake where one can hire a rowing boat - great fun for the children! There is a monument to the victims of the Madrid 3/11 terrorist bombings, the Forest of the Absent, and the Crystal Palace, a large structure entirely made of glass. Sunday afternoons in summer are a treat in the park, where young hippies play bongos and dance.
Naval Museum of Madrid
A beautiful museum with a large interesting collection about Spanish naval history, from the efforts of kingdoms of Aragon and Castilia, the many successes and few failures (what's known in English as the defeat of the Spanish Armarda has a section) in the 15th-17th centuries, the drastic decline in the 19th century and its consequences in terms of losing the country's empire, the division of the navy into opposing sides in the 1930s Civil War, to today. It's almost all labelled in English as well as Spanish.
A temporary exhibition traces today's Spanish flag from its origin as the navy's attempt to have one that contrasted well with other navy's flags, and the museum has the very large flag flown by the Spanish flagship at the Battle of Trafalgar (the loss is blamed on the French admiral for insisting on sailing out of Cadiz to fight it!)
A massive roundabout at the intersection of Calle de Alcala and Paseo del Prado, this plaza houses one of Madrid's emblems, the Fountain of Cibeles, which portrays the Roman goddess of fertility sitting upon a chariot pulled by two lions. On the southeast corner dominating the Plaza is one of the world's most beautiful city halls, the Palacio de Cibeles (formerly the Palacio de las Comunicaciones), an impressive structure with a jaw-droppingly spectacular façade. Inside, the building holds a cultural center with changing art exhibits and info on Madrid, and you can climb to the upper floors for some excellent views out the window. On the southwest corner of the square sits the imposing Bank of Spain (Banco de España) building, while the northeast corner is home to the Palacio de Linares, which holds the Casa de América, a cultural center with an art gallery of Latin American works.
Royal Botanical Garden of Madrid
Established in 1755, the garden has been in its current location since 1774. Its extensive collection is dispersed over seven sections, five greenhouses, and a herbarium. A map of the garden is available here.
Prado Museum
One of the finest art collections in the world and the best collection of classical art in Madrid. It includes many different collections: the Spanish (El Greco, Velázquez, and Goya), the Flemish and Dutch (Rubens, van Dyck, and Brueghel), Italian (Botticelli, Tintoretto, Titian, Caravaggio, and Veronese) and German (Albrecht Dürer, Lucas Cranach, and Baldung Grien).
Some highlights not to miss at the Prado include the Bosch masterpiece The Garden of Earthly Delights, Velázquez's masterpiece Las Meninas, the Black Paintings, The Third of May 1808, and a pair of paintings known as The Clothed Maja and The Naked Maja by Goya, Adoration of the Shepards by El Greco, and David with the Head of Goliath by Caravaggio. Be sure to walk along Paseo del Prado, a pedestrian walkway full of fountains and trees near the museum.
Visitors can bypass the often extremely long queues by purchasing tickets beforehand by phone or online, for an additional €.90 fee per ticket. Tickets purchased online can be printed or downloaded onto a smart phone; all pre-purchased tickets can be picked up (with a reference number) or presented at the main (Jerónimos) entrance in the northeast corner of the building. If you are planning to spend a full day at the museum, it is possible to leave (e.g. for lunch) and reenter by getting your ticket stamped at the 'Educación' counter just inside the main entrance.
An affordable café and cafeteria-style restaurant are on the ground floor, along with a gift shop. No food, drinks, backpacks or umbrellas are permitted (a bag check is just inside the main entrance). Photography not permitted.
Thyssen-Bornemisza Museum
Contains a large art collection including masterpieces by Monet, Goya, Degas, Renoir, Van Gogh, Picasso, Mondrian, Bacon and Lichtenstein.