Oaxaca

A hilltop was cut flat and a Zapotec city raised on the platform. One building mid plaza sits at an angle to the rest and is read as an observatory.

Gilded carving covers the entire ceiling, including a family tree worked as figures. The monastery beside it now houses the cultural museum.

Mineral water running over the cliff has hardened into what looks like a stone waterfall. Sitting in the pools at the top puts the valley below your feet.

Walls are filled with small cut stones set into geometric patterns without any mortar. More than twenty designs appear, and on some walls no pattern repeats.

A girth of 42m puts it among the thickest trees anywhere. Its age is put at around fifteen hundred years, and it stands in a churchyard.

One wing of the covered market is given over to grilling meat, and the smoke fills it. You buy meat by weight and sit down beside the grill with tortillas.

Wool is dyed with insects and plants and woven by hand in this village. The red comes from an insect living on cactus, and the process is shown to visitors.

Sealing the kiln to cut the oxygen turns the clay black during firing. The shine has to be rubbed onto the surface with a stone before it goes in.

Wood is carved into imagined animals and painted in dots and lines. One piece can take weeks, so the price follows the pattern rather than the size.

At the turn of October into November candles are lit in the cemeteries and families sit with the graves right through the evening. It is a family occasion, so asking before photographing is the courtesy.

Plants from Oaxaca state alone, set out in the old orchard behind the Santo Domingo monastery. You walk among tall columnar cacti and agaves with a guide explaining their uses. There is no self-guided entry, only tours, and English ones run less often.

The pedestrian street running from the Zocalo up to Santo Domingo church. Most buildings along it are of the region's pale green stone, which deepens in colour after rain. Galleries and textile shops line it, and street performers gather in the evening.

The central square, its bandstand shaded by huge laurel trees, with the green-stone cathedral on one side. From the arcade cafes around it, balloon sellers and bands pass by in turn. Protest camps often pitch tents here too.

A 17th-century Baroque church for the Virgin of La Soledad, patron of Oaxaca, its facade carved in tiers like a folding screen. Her feast falls on 18 December. Ice cream stalls line the stepped plaza in front, crowded after Mass.

Usually held on the two Mondays after 16 July in the open-air auditorium on Fortin hill. Dance troupes from the state's eight regions perform in traditional dress, then throw fruit and bread into the stands. The front seats are ticketed and sell out early.

A Zapotec hill fortress-town just off the Mitla highway. Below lies one of the biggest ball courts in Mesoamerica, and climbing to the citadel opens the whole valley. With nearby caves it was inscribed by UNESCO in 2010, and visitors are few.

A big market held every Sunday in a town about 30km east of Oaxaca. People from the surrounding villages come to shop, so locals far outnumber tourists. Inside, lamb barbacoa is cooked and mezcal is poured as tasters.

The southern valley town of Ocotlan holds its market every Friday. Rodolfo Morales, a painter born here, restored the Santo Domingo church on the square, and his former home serves as a gallery. Painted clay figures from a nearby village reach the market too.

A town whose sign proclaims it the world capital of mezcal, with distilleries lined along the highway. Many show the whole process, including a horse-drawn stone wheel crushing the roasted agave. Tastings keep coming, so pick someone to stay sober and drive.

An 18th-century building turned museum, rotating displays of the cloth that differs village by village across Oaxaca state. Dye sources such as cochineal and indigo are shown alongside. Admission is free; the shop sells pieces under the weaver's name.

A 16th-century Dominican monastery left unfinished, its roofless basilica a row of stone columns open to the sky. Independence hero Vicente Guerrero was executed here in 1831. It lies some 20 minutes south of town, and tour groups rarely come.