WASHINGTON — The attention London receives this summer is sure to include the kind of glossy public relations usually associated with hosts of the Olympic Games. Surely the script is already written. Here is a modern metropolis with deep roots in the past, a city that eagerly embraces all the earth’s diversity, that operates with magical efficiency, that brings to bear the most advanced technologies, that celebrates with all its might the world’s elite athletic competitors.


But that Olympic veneer has little to do with why we should care about London in the first place, which is why we are lucky the Folger Shakespeare Library here has chosen to add its quiet, studied voice to the season’s festivities with its exhibition “Open City: London, 1500-1700.” We should care, the show suggests, because of a more profound role London has played in world culture by shaping ideas of what a great city can be.


At first glance the exhibition makes the claim seem mighty unlikely. Could those antique centuries really have so much to do with the three centuries that followed? Sure, in 1500 London was a modest city with nearly all its 50,000 residents living within its medieval walls, and in 1700 London had 10 times the population. But look closely at the show’s maps, histories, plays, proclamations, ledgers and letters, along with facsimiles of rare documents from the British Museum, and try to find a great city taking shape in the midst of the foolishness, brutality, dogma and trauma.


In the 1530s King Henry VIII dissolved the city’s monasteries, doling out their property to favorites, some of whom carted away relics to use in constructing their aristocratic manses.


Attitudes toward religious practice shifted so violently that they can be traced in the fate of Edmund Bonner, who was made bishop of London by Henry VIII when the English church was Roman Catholic. Henry’s son, Edward VI, imprisoned Bonner for not using the Protestant Book of Common Prayer; Edward’s Catholic sister, Mary, reinstated him as bishop; Mary’s sister, Elizabeth, imprisoned him yet again.


At the time, church worship was not only uniform (established by the monarchy), it was also mandatory, with an exemption offered to foreign diplomats.


And then there was the 17th-century civil war. A striking panoramic view of London here by Wenceslaus Hollar shows the city in triumphant expanse, but the map was published in 1647, when King Charles I was imprisoned and London was almost a parliamentary military garrison.


Meanwhile, London’s public market in Cheapside was so marked by fraud and vice of all kinds that an early-17th-century play by Thomas Middleton, shown here in an early edition, is about the impossible: “A Chast Mayd in Cheape-Side.” She is named Moll (prostitute) and is married off to a suitor named Whorehound.


By the 1640s the government had grown so wary of the liberties of the London stage that a parliamentary act suppressed “publique Plays and Play-houses, Dancing on the Ropes, and Bear-baitings.”


Amid these controversies and censorship, there was also disease. A 1625 proclamation from Charles I calls off London’s three-day Bartholomew Fair to ensure “universall safety” because of the plague. And from 1665 we see a listing of the causes of death for all Londoners that year; of the 97,306 burials, 68,596 were attributed to the plague.


The next year, though, came the real apocalypse. The Great Fire of London in 1666 destroyed much of the city: 273 acres were laid waste, 130,200 houses burned, 11 parish churches survived out of 89. A 1666 map here by Hollar is shocking, as if the entire center of a metropolis had been excised.


How, in the midst of all this, did a great city emerge? The exhibition’s curators, Kathleen Lynch, executive director of the Folger Institute, assisted by Elizabeth Walsh, head of reader services at the Folger, argue that during these two centuries, transformations took place in three major public arenas, “gathering places where people mixed for business, leisure and worship”: church, the theater and the market. And that those changes created an “open city.”


The case builds indirectly — almost too indirectly, as display cases narrowly focus on, say, the fate of St. Paul’s Cathedral or the development of Covent Garden. But gradually the argument takes shape and the transformations of religion, culture and commerce intertwine.


When Henry VIII dissolved the monasteries, for example, the unity of the church was challenged. The king was not seeking to stimulate debate; he was seeking a new form of conformity. But he demonstrated the possibility of altering the unalterable, thus leading to the back-and-forth extremes of the following century, calling into question ideas about the established church’s relationship to the state.