There is a library, where all the theses that past students have written are stored, for reference, but Ulivieri does not assign set texts. “Football moves too fast,” he said. “By the time a book on tactics is published, it is already old.”

Instead, he encourages his pupils to think. In “The Italian Job,” the memoir of the former Chelsea manager Gianluca Vialli, Lippi, the coach who led Italy to the 2006 World Cup title, remarked that “Coverciano does not offer truths, but possibilities.”

There are lectures, on the finer points of tactics, but they are hardly formal. “They can interrupt me whenever they like,” Ulivieri said. The sessions, he said, are more like discussion groups. The students have notebooks, but they are encouraged at the end of each day to record their own observations, “the things they liked and did not like.” Ulivieri wants his students to learn from one another; Lippi has said he considered that “exchange of ideas” the most important part of his time here.

Much of the teaching has a practical edge: not just the days on the training field and the visits to elite clubs — this year’s group spent time at Juventus, Inter Milan and Borussia Dortmund, and also the nearby Serie B team Perugia — but in video sessions.

“We watch a lot of games together,” Ulivieri said. “I will tell one student he is in charge of the home team and another to manage the away team. I will pause it after 15 minutes and ask what they should do. They will say, ‘We’re doing O.K., I’ll leave it.’ Then we watch another 15 minutes. We pause it. ‘O.K., what do you do now? And you?’”

This is the message Ulivieri wants his students to comprehend: Every game is dynamic, fluid, in a perpetual state of flux. Things change, and so must the coaches. He likes to see managers “who take the game in hand,” who adjust and alter and tweak as the situation demands.

He draws out his own notebook to illustrate the point. “If our opponents have two really good central defenders,” he said, sketching out a formation, “and we have two good strikers, then they can cancel us out.”