After an 18-month, $85 million overhaul, the Delacorte Theater reopens next month with a starry new version of “Twelfth Night.” I’ll leave it to playgoers and critics to deliver their verdicts on the production.

I’m happy to report, in the meantime, that the renovation deftly fixes much of what ailed the city’s beloved home of free Shakespeare in Central Park.

It was on its last legs before it was shuttered. Built during the Kennedy era for the current price of a two-bedroom condo in Fort Lee, N.J., the Delacorte from Day One was a glorified, rickety high-school grandstand, with water leaking into ramshackle dressing rooms and raccoons nesting backstage. Watching great actors and directors put on “Hamlet” there was roughly akin to consuming truffled langoustine on the L train.

The modesty was part of its charm. Like the park, it spoke to the city’s egalitarian soul and cultural ambition. Its makeover is the latest change to a park that has recently undergone, or is considering, a variety of alterations, which include the opening of the excellent Davis Center in Harlem, plans to revamp Wollman Rink and a proposal by the Metropolitan Museum to replace an old wing with a new one, a stone’s throw from the Delacorte.

It may seem odd to think of Central Park as a work in progress. It can come across as a grand relic from another century. But this middle stretch of the park in particular, which includes the Delacorte, has undergone a surprising number of upheavals over the past 200-odd years that mirror changes across the city.

The much-improved Delacorte is cone-shaped now, wider at the top, blending more discreetly into its leafy copse of cherry, sycamore and hornbeam, beside the Great Lawn. The clunky old clapboard drum and flimsy skirt canopy are gone, swapped out for rustic, handsome, tongue-and-groove, reclaimed redwood planks and a marquee that finally gives what had been a comically modest entrance a sense of occasion.

The architect in charge of the makeover, Stephen Chu, has repurposed the redwood from 25 decommissioned city water towers, a nice touch. He left some of the old water stains to give the new facade an instant patina.

And all manner of backstage upgrades should help streamline operations, which will allow the Public Theater, the Delacorte’s owner, to stage more performances each summer. That means thousands more playgoers, many from far-flung neighborhoods where the Public takes its mobile unit and distributes tickets, should get to see Shakespeare in the 1,864-seat amphitheater.

In 1962 the Delacorte rose on the spot where the Brooklyn-born Joseph Papp, a few years earlier, had staged a pop-up production of “Romeo and Juliet” from a flatbed trailer that he hauled behind a garbage truck. He opened the Delacorte with a “Merchant of Venice” starring George C. Scott and James Earl Jones.

It was a message to commercial Broadway: A true cosmopolis makes great art and culture free and available to everyone.

But by the 2010s the theater was falling apart. The bleachers were a sieve. Seats were cramped, wheelchair access miserable and way-finding a joke.

Backstage was even worse — a deteriorating warren of chain-link cubicles with tarp coverings that failed to keep out the rain. Some actors declined roles because of the conditions. The Public forked over a king’s ransom each spring just to clean up after raccoons that sheltered in winter under the open bleachers, gnawing through wiring, leaving the scattered remains of half-eaten turtles from nearby Turtle Pond.

So in 2018 the Public enlisted Bjarke Ingels, the Danish architect, to draw up a plan for a new theater with a retractable roof that could operate through the shoulder months or even year-round. Cost estimates started at $120 million.

The Central Park Conservancy, the Parks Department and various community boards neighboring the park were quick to make clear that would never happen: They didn’t want a bigger theater with a longer calendar. Then Covid arrived. The optics were poor for an arts nonprofit spending a fortune on an architectural showpiece in the midst of a pandemic that hit the theater world especially hard.

So the Public turned to Chu, a partner at Ennead, the New York architecture firm, who had helped revamp the company’s landmark home on Lafayette Street in the former Astor Library some years ago.

Chu’s assignment was to tread a line: modernize the Delacorte’s back-of-house while preserving what New Yorkers had come to appreciate about its let’s-put-on-a-play vibe.

Was this a missed opportunity?

Once upon a time, New York built the Brooklyn Bridge, the 42nd Street Library and Central Park itself. Great public architecture spoke to the city’s grandest ambitions and democratic ideals. Upgrading a ’60s band shell was not going to result in anything lofty.

And it hasn’t.

But for $85 million — about half of that money comes from city funds — Chu and his Ennead colleagues have produced a 21st-century facility that no longer sticks out in the park like a double-wide trailer on Billionaire’s Lane in Southampton. They’ve preserved the Delacorte’s wondrous city views beyond the stage and made prosaic but crucial changes, too, like adding wider seats, increasing wheelchair access and swapping out miserable bathrooms for new ones.

Papp’s postwar project to make available the finest New York had to offer free of charge was the argument made a century earlier by Olmsted and Vaux, Central Park’s genius architects, when they designed what remains the city’s most sublime work of public art and stagecraft.

They planned and planted nearly every tree, hill, meadow and blade of grass in Central Park. But it was not until nearly World War II that the acreage occupied by the Great Lawn and Turtle Pond, where the Delacorte rose, took its current shape.

That’s because the area had belonged, since before the park was built, to a massive, fortlike reservoir for the Croton Aqueduct. The aqueduct and its reservoirs remapped 19th-century New York. In the late 1700s and early 1800s tanneries in Lower Manhattan poisoned the downtown water supply, spreading cholera, killing residents and causing many to flee.

In response, New York built the Croton Aqueduct to bring clean water from more than 40 miles upstate and hastened northward expansion in Manhattan to where reservoirs landed. Some 250 mostly Black but also Irish and German residents established a community called Seneca Village in a swampy, rocky area just beside the reservoir.

City Hall then bought out residents, using eminent domain, and demolished Seneca Village to make way for Central Park in the 1850s. The displacement belonged to a history of relocating Black and immigrant communities in the city.

And in time, New York’s water infrastructure moved mostly underground. By 1917 the reservoir was deemed obsolete, opening debate over what to do with the doughnut hole it left in the park. Discussions dragged on for years. There was talk about a sports arena, an opera house. With the Depression, the derelict site became a Hooverville.

Finally the city settled on an oval-shaped meadow bracketed by playgrounds and playing fields to the north and, to the south, a new body of water for turtles at the base of a rocky outcrop where shrubs and wildflowers attracted migrating warblers.

Papp arrived in his garbage truck barely a generation later. Robert Moses and a Red-baiting deputy he had put in charge of Central Park opposed the Delacorte idea. They suspected that Papp, with his free Shakespeare for the masses, was a Communist.

Papp’s victory over the Power Broker makes for a juicy chapter in Robert Caro’s biography of Moses. An era of People Power and counterculture dawned, reshaping the park, the theater world and New York. For Papp, the pastoral setting made up for whatever bells and whistles a fancy Broadway theater could supply.

Which is why the Delacorte’s low-key, rustic renovation ultimately seems right. “All the world’s a stage” is a line from “As You Like It,” the comedy in which a duke, banished to a forest, discovers in nature values of equality and humanity lost at the court. It’s in part about rural versus urban society — and the need to find harmony.

Patrick Willingham, the Public’s executive director, told me the other day that he still sees raccoons scampering in and out at the theater. There’s no way, he acknowledged, to fully quarantine the Delacorte: It and the park share the same ecology — and send a similar message about openness and New York.

A friend sent me a picture from Smithsonian Magazine in late June by two photographers who had captured a pair of coyotes sunbathing in the new Delacorte’s bleachers. The coyotes have apparently also become regulars, according to Willingham.

He says everyone at the theater now calls them Romeo and Juliet.