Stand in the Plaza Mayor and work out why it is irregular — it grew round penned livestock rather than being designed

Look at the tiered wooden galleries and work out that they were built as balconies to watch animals from

Come when the square is sanded for a bullfight or a festival and see what it was always for

Find out that this square played the Spanish bullring in Around the World in Eighty Days, with much of the town as the crowd and Cantinflas as the matador

Climb to the castle ruins and the old church above the town for the view over the Tagus valley

Chinchón's Plaza Mayor is irregular rather than laid out, because it grew: livestock were penned around the houses so their owners could watch them from the balcony without going outside, and that is why the whole square is ringed with tiers of open wooden galleries on stone columns. It is protected as a Historic Ensemble. Several times a year the ground is sanded and the square becomes a bullring, which is what those balconies have always been used for, and the rest of the time it is where the town eats.

Chinchón: The Square That Is Still a Bullring

Stand in the Plaza Mayor and work out that the stone under your feet came from the edge of the town

Go and look at the quarries, which supplied a great deal of Madrid as well as this square

Find out what a tinaja is and why making them was an industry here

Go to the Ulpiano Checa museum and find out who he was

Work out the reversal: the second town of the province in the 19th century, and what it is now

Colmenar de Oreja was, until well into the 19th century, the second most populous town in the province of Madrid after the capital itself — built on stone quarrying, the making of tinajas, wax, esparto, textiles and farming. Its Plaza Mayor is a large arcaded square of local stone, and the quarries that supplied it and much of Madrid are on the edge of the town. The painter Ulpiano Checa was born here and has a museum. Nine wineries work under the Vinos de Madrid designation, in the Arganda subzone.

Colmenar de Oreja: A Town Built of Its Own Quarry

Walk the Jardín del Príncipe and the Jardín de la Isla and work out that the water system is the actual monument

Find the historic dams and irrigation channels — this is a landscape engineered over centuries, not a park

Find out what happened in March 1808 and why it ended Godoy and Charles IV

Work out that until the mid-18th century nobody outside the court was allowed to live here, and the town was then founded from nothing

Eat the strawberries and asparagus the huertas here have been supplying to Madrid for centuries

What UNESCO listed at Aranjuez in 2001 was not the palace but the Cultural Landscape — the whole system of gardens, market gardens, canals, irrigation channels and historic dams laid over a wide valley where the Tagus meets the Jarama. For most of its life ordinary people were not allowed to live here at all; Ferdinand VI lifted that in the mid-18th century and a town was founded from nothing. In March 1808 the Mutiny of Aranjuez brought down Godoy and forced Charles IV to abdicate, and the town still re-enacts it every year.

Aranjuez: A Royal Landscape, Not a Royal Palace

Walk the planned centre and work out that the palace, church and workshops were designed as one building

Find out who Churriguera was and why the family name became a word for a whole style

Work out what was made here: a glass factory founded from nothing, with a town built round it between 1709 and 1713

Work out why the church is dedicated to Francis Xavier, and what that says about where the founder came from

Work out where Goyeneche came from and why the town is named after a Navarrese valley

Juan de Goyeneche was a Navarrese businessman from the Baztán valley who, at the beginning of the 18th century, decided to build an industrial town from nothing east of Madrid — a palace, a church and workers' housing on an orthogonal grid, designed as one scheme by José Benito de Churriguera between 1709 and 1713. It was built around a glass factory Goyeneche founded from nothing, and Spanish urbanists including Fernando Chueca Goitia have called the layout a model of native Baroque town planning. The palace and its church, dedicated to the Navarrese saint Francis Xavier, have been protected as a cultural asset since 16 March 2000.

Nuevo Baztán: A Baroque Company Town

Visit the Prado, opened in 1819, and find Velázquez's Las Meninas of 1656

See Picasso's Guernica of 1937 in the Reina Sofía

Tour the Thyssen-Bornemisza Museum in the Villahermosa Palace, opened in 1992

Three world-class collections stand within about a kilometre of each other on the Paseo del Prado. The Prado opened in 1819 and holds the Spanish royal collection — Velázquez, Goya, Bosch, Titian — with Las Meninas of 1656 at the centre of it, a painting that has been argued about for three hundred and seventy years and still is. The Reina Sofía has Guernica, painted in 1937 for the Spanish pavilion in Paris and kept out of Spain until Franco was dead. The Thyssen fills the gaps both of them have, which is most of the rest of European painting.

Madrid's Paseo del Prado: The Prado, Guernica and the Thyssen

Go into the university's Paraninfo and the Plateresque facade Cisneros paid for

Find out what the Complutensian Polyglot Bible was, and that it carried the first printed Greek New Testament and Septuagint

Go into the house where Cervantes was born and sit on the bench outside with him and Sancho

Work out the gap: the university was suppressed in 1836 and moved to Madrid, and the town had none until 1977

Walk the Calle Mayor — 396 metres, the longest street in Europe still arcaded on both sides, with an upper gallery that once let Jewish households reach each other without going down into the street

Cardinal Cisneros founded the university here on 13 April 1499, and what came out of it was the Complutensian Polyglot Bible — Hebrew, Greek and Latin in parallel columns with some parts in Aramaic, the first polyglot edition of a complete Bible, carrying the first printed editions of the Greek New Testament, the Septuagint and the Targum Onkelos. Cisneros bought the manuscripts himself and brought in the best theologians he could find. Cervantes was born in the town. The university was suppressed by royal order on 29 October 1836 and moved to Madrid, and Alcalá only got one back in 1977. UNESCO made the city a World Heritage Site in 1998.

Alcalá de Henares: Cervantes and the Polyglot Bible

Find the Palatine Stradivarius, the palace's set of instruments

Cross to the Almudena cathedral, dedicated to the Virgin of the Almudena, patron of Madrid

Walk the Plaza de Oriente to the Teatro Real on the far side, facing the palace

The Royal Palace in Madrid is the official residence of the King of Spain, though the royal family lives at the Zarzuela; with 135,000 square metres and 3,418 rooms it is the largest royal palace in Western Europe. Philip V had it built on the site of the old Alcázar, which burned almost completely in 1734: work began in 1738 to plans by Filippo Juvara, carried on by his pupil Sacchetti and finished by Francesco Sabatini, and Charles III was the first king to live in it. Its collections include the Palatine Stradivarius instruments. Across the square stands the Almudena cathedral, dedicated to the patron of Madrid, and at the far end of the Plaza de Oriente the Teatro Real faces the palace.

Madrid's Royal Palace: 3,418 Rooms on the Site of the Alcázar

Go into the church and find the grille made by the Carthusian monk Francisco de Salamanca

Find the walnut choir stalls carved in the 16th century, removed to Madrid in 1883 and returned here in 2003

Work out the founding story: a king who burned a charterhouse in France and built this one in 1390 to make up for it

Walk the Lozoya valley around it, which is inside the Sierra de Guadarrama National Park

Cross to the Puente del Perdón and find out what it was called that for

Henry II of Castile ordered a charterhouse built in the Lozoya valley in 1390 — the first Carthusian foundation in Castile — and tradition says he chose that order because his own army had burned one of their houses during the war in France. He picked the spot himself, beside a hermitage already there, and told his son, the future John I, exactly where. It was Carthusian until 1835. The grille separating the congregation from the monks was made by a Carthusian monk, Francisco de Salamanca, and the 16th-century walnut choir stalls were taken to Madrid in 1883 and only brought back in 2003.