All the superlatives apply to the marine salvage operation about to unfold off the Italian island of Giglio: largest, most expensive, most complicated. And first of its kind.

In an unprecedented feat of engineering that could make history or fail catastrophically, teams will begin Monday morning to hoist the wrecked Costa Concordia, which has been resting on its side atop two rocks near an ocean cliff for the last 20 months. The project’s anticipated price tag: nearly $800 million.

Called “parbuckling,” the job involves a complicated system of 56 enormous cables, 58 pulling machines, 11 multistory flotation tanks, six undersea platforms and 1,180 grout bags full of cement. Weather permitting, the process is scheduled to begin at first light on Monday in Italy, or roughly 1 a.m., Boston time — 16 months after the initial work at the site began, and 20 months after the shipwreck in which 32 people died.

“If it doesn’t work, then I don’t think anybody can say it’s because we did this wrong or that wrong,” said Mark Hoddinott, general manager of the London-based International Salvage Union. “They’ve done everything right. Now they’re going into this area where this has never been done with a ship this size before.”

Nick Sloane, the salvage master at Titan Salvage in Pompano Beach, Fla., has been overseeing the operation on Giglio that involves more than 500 workers and continues 24 hours a day, seven days a week.

“We’ve managed to increase it to eight days a week now, give us a bit more time,” he said. “It’s a full-time operation; you can’t afford to stop for anything.”

Initial plans called for the wreck to be removed by May 2013. In retrospect, Sloane called that time line “unrealistic,” highlighting the complication of bad weather during the winter and the difficulty of drilling into granite underneath the ship.

“Basically, the plan’s modified quite a bit,” he said. “We’re already on Plan C or D … We’ve been adapting this the more we learn about her. We think we’ve got it just about right now.”

Officials say the rotation of the ship, a tense balancing act, could take 10 to 12 hours.

“There will be a lot of noise, there will be a lot of minor steel parts that are going to break apart,” Sloane said. “It’s going to be quite a slow operation.”

While parbuckling as an engineering concept has been historically used to right ships, it’s never been tried with one so large. There is no option to start over or change gears if something goes awry.

First, the ship must be pulled free of the rocks, a difficult task because the hull has wrapped itself around the reef where it rests. Then, the winches will continue to pull the ship until the flotation tanks, called sponsons, reach sea level and can be filled with water. The water will help push the ship down to the platforms that await on the sea floor.

All the while, crews aboard a nearby barge will be monitoring the ship and making fine adjustments to the operation as needed. No one will be allowed to come onto the island or leave during the process, and nobody will be allowed in the water around the ship or on the ship.

There will, however, be a huge audience. As of Friday, more than 300 members of the media had registered to cover the parbuckling from Giglio.

Tim Donney, head of marine risk consulting for Allianz Global Corporate & Specialty, said that if the operation fails, the consortium would have to submit new plans to authorities — one of which could include cutting the vessel up.