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

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 ducal palace where Ana de Mendoza spent her last years and died in 1592

Find out what happened between Ana de Mendoza and Teresa of Ávila, and why Teresa pulled every nun out of the town

Go into the collegiate church for the four tapestries — eleven metres by four, woven at Tournai, recording Asilah and Tangier in 1471

Work out what makes them unusual: the first tapestry series to narrate contemporary politics in this kind of detail

Walk the two quarters of the town, the old and the ducal, which were laid out separately

Ana de Mendoza, Princess of Éboli by her marriage to Philip II's favourite Ruy Gómez de Silva, was one of the most powerful women in Spain — she and her husband founded two Discalced Carmelite convents here, then fell out so badly with Teresa of Ávila that Teresa ordered every nun out of Pastrana and left her alone in them. Ana died here in 1592. The collegiate church holds four silk and wool tapestries averaging eleven metres by four, woven in the Paschier Grenier workshop at Tournai on the order of Afonso V of Portugal, recording his conquests of Asilah and Tangier in August 1471 — the first tapestry series to narrate contemporary political events in this kind of descriptive detail.

Pastrana: A Princess Under House Arrest

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

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

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

Come in late February or March for the floración and get to a mirador above the valley floor

Work out the scale: tens of thousands of stone-fruit trees flowering within a couple of weeks of each other

Go to Medina Siyâsa above the town, an excavated Andalusi settlement with reconstructed houses

Find the rock art in the Almadenes gorge, part of the Levantine rock art World Heritage listing

Canoe or walk the Segura through the Almadenes cut

Cieza sits on the middle Segura where the river cuts through the Murcian hills, and it grows peaches, nectarines and apricots on terraces across the whole valley floor and up the slopes. For two to three weeks in late February and March the entire valley flowers at once — tens of thousands of trees in pink and white against bare rock — and the town has built a set of viewpoints and marked routes specifically to look at it. The rest of the year the same valley holds Iberian rock art in the Almadenes gorge and a Muslim town site at Medina Siyâsa.

Cieza: The Blossom of the Segura Valley

Walk the wall — 11th-century Moorish work restored in the 15th, and one of very few surviving circuits in the Madrid region

Work out how the defence works: the wall on one side, the Lozoya wrapped round the other three

Go into the Picasso museum and work out how a small town on the Lozoya came to hold a collection like it

Find out who Eugenio Arias was — a barber from Buitrago, and a friend of Picasso

Go into the 15th-century Gothic-Mudéjar castle and the church of Santa María del Castillo of 1321 beside it

Buitrago is one of very few towns in the Madrid region to have kept its walls — Moorish, 11th century, restored in the 15th — on a peninsula with the Lozoya running round it. Inside is a Gothic-Mudéjar castle of the 15th century, the church of Santa María del Castillo of 1321 in the same style, and, unexpectedly, a Picasso museum. Eugenio Arias was a barber from this town and a friend of the artist, and the collection he built is now held here.