Palacio de Bellas Artes

Porfirio Díaz commissioned a new national theatre for the centenary of independence and gave it to the Italian architect Adamo Boari in 1904. Boari designed an Art Nouveau palace in Carrara marble, and then the ground gave way: the structure, standing on the soft bed of the drained lake, began sinking under its own weight. Work slowed, the Revolution broke out in 1910, Boari left, and the shell stood unfinished for two decades.

Federico Mariscal completed it between 1930 and 1934 in the style of that moment, which is why the building changes language as you walk in: Art Nouveau marble outside, Art Deco in coloured Mexican stone inside, with geometric masks and ironwork that belong to a different decade from the facade. It opened in 1934, twenty-nine years after it was begun, and it has gone on sinking — the entrance is now several steps below the level of the street it was built to face.

The glass curtain

The theatre's fire curtain is a stained-glass panel of the two volcanoes, Popocatépetl and Iztaccíhuatl, assembled by Tiffany Studios in New York from nearly a million pieces. It is lowered before performances and shown at some guided sessions; it is not on view to museum visitors as a matter of course, which is the single most common disappointment reported here.

*Diego Rivera, Man, Controller of the Universe (1934).* The most famous thing in the building, and a reconstruction: Rivera painted the original for the Rockefeller Center in New York in 1933, included a portrait of Lenin, refused to remove it, and the fresco was destroyed. He repainted it here the following year, larger and less diplomatic. Look for the two halves of the composition — capitalism and socialism — and for the portraits of Rockefeller and Trotsky facing each other across it.

*José Clemente Orozco, Katharsis (1934).* A machine-age vision of destruction, the counter-argument to Rivera's faith in progress. Orozco is the darkest of the muralists and the least quoted; standing between the two of them is what makes this floor worth the MX$95.

David Alfaro Siqueiros, whose panels here — including New Democracy — use the foreshortening and industrial paint he experimented with all his life; the figures lunge out of the wall. And Rufino Tamayo, whose two works are the quietest and most abstract, and the reason the floor does not read as a single political statement.

An hour covers the murals properly. The temporary exhibition halls on the same floors are worth another thirty minutes if the show is good — they have held major international retrospectives — and the museum publishes what is on through INBAL's own listing rather than a fixed calendar.

The Ballet Folklórico de México de Amalia Hernández has performed in this hall since the 1950s: regional dances staged with an orchestra, in a theatre most audiences would pay to sit in regardless of what was on it.

Performance days move month to month, so read the venue's cartelera rather than any fixed timetable, including ours. Tickets go through Ticketmaster with handling fees on top. The palace also programmes opera, the national symphony and visiting companies — the same hall, the same glass curtain, usually cheaper.

INBAL's listing for this museum states free entry on Sundays for the whole public — domingos entrada libre a todo público — with no nationality or residency test. That is different from the INAH museums — Anthropology, Chapultepec Castle, the Templo Mayor, Teotihuacán — where Sunday is free only for Mexican nationals and foreign residents.

So if you are a visiting foreigner building a Sunday, this is the museum to build it around: MX$95 saved, the mural floor at its busiest but still walkable, and the rest of the Centro Histórico free anyway. Free entry also applies any day to students and teachers with a current credential, over-60s with an INAPAM card, and children under 13.

The view down onto the tiled dome, with the Torre Latinoamericana behind it, is shot from the terrace of the café on the upper floor of the department store on the corner of Eje Central and Avenida Juárez. Entry is free, you are expected to buy a coffee, and the queue for the terrace runs longest between five and seven in the evening when the light is best. Go up before the light rather than during it.

The other elevated view is from the Torre Latinoamericana observation deck, which is higher, further away and charges MX$220. Between the two, the free terrace has the better composition and the tower has the better sense of the city's size. The Alameda Central park across Juárez gives the whole facade from ground level, which is where the marble reads best in the morning.

Walk from the Zócalo down Madero — twelve minutes, pedestrianised — and take the museum before lunch, when the mural floor is quiet. Afterwards the Torre Latinoamericana is three minutes away and the Alameda is across the road.

If you can arrange it, come back at dusk: the terrace café across Eje Central gives the dome in the last light, and the palace is floodlit from the outside afterwards. On a Sunday, do the reverse — get here at opening while it is free, then let the crowd arrive behind you. The whole first day is on the one-day itinerary, and the rest of the trip on the independent Mexico City guide.