“Like the stock market, Alexander Hamilton has hit recent highs,” the president of the Gilder Lehrman Institute of American History, James Basker, told a crowd of history buffs gathered in Trinity Church.

The event was a sneak preview of the “American Experience” film “Alexander Hamilton,” which will make its premiere on Monday on PBS. As Mr. Basker noted, the timing of the film is serendipitous: After long being caricatured as an elitist, and compared unfavorably with his political rival, Thomas Jefferson, Hamilton is now enjoying the benefits of historical revision.

The Gilder Lehrman Institute, which co-sponsored the event last Wednesday evening with “American Experience,” has played a significant role in the Hamilton revival. Mr. Basker was the projects director of the Alexander Hamilton exhibition that opened at the New-York Historical Society in 2004, and of which smaller versions have been traveling the country since.

The film, which includes dramatizations by prominent actors and interviews with historians, reflects the new attitude toward Hamilton. The film’s writer, Ronald Blumer, and the actor playing Hamilton, Brían F. O’Byrne, portray Hamilton sympathetically — as brilliant, devoted to his country, and sincere, if also stubborn and indiscreet.

Born on the island of Nevis in the Caribbean, Hamilton was a bastard and therefore not allowed to attend the local Christian school. He moved to St. Croix when he was 10, whereupon his father abandoned the family, and his mother died shortly afterward of yellow fever. At 14, Hamilton became a clerk for an American trading company; he educated himself at night from the classical histories in his mother’s library, his sole inheritance. He worked his way up at the company so impressively that eventually a group of influential people raised funds to send him to the American Colonies to be educated. He arrived in New York in 1773 and immediately joined the Revolutionary cause.

As the historian Willard Sterne Randall says early in the film, “Hamilton is the only one of the Founding Fathers who was an outsider: an orphan, an immigrant, a scholarship boy, a college dropout.”

If Hamilton in the film is easy to admire, Jefferson is easy to hate. Played with a supercilious sneer by Daniel Gerroll, Jefferson comes across as an aristocrat with a misguided view of America’s future as an agrarian idyll with a weak central government. In the 19th century, the country would become something much closer to Hamilton’s vision: a financial and industrial superpower.

Washington made Hamilton his Treasury secretary and Jefferson his secretary of state, and the two quickly became locked in a battle over the direction of the country. In the section of the film that depicts this struggle — which led to the rise of the nation’s first political parties — Jefferson attacks Hamilton in terms that seem to reflect his own class snobbery:

“I will not have my reputation slandered by a man whose history — from the moment that history stooped to notice him — is a fabric of machinations against the liberty of this country — a country which not only received him as a penniless immigrant and gave him food, but now heaps honors on his head.”

The three historians who spoke after the preview on Wednesday — Carol Berkin, Joanne Freeman, and Ron Chernow — all expressed their admiration for Hamilton, and frustration with the myth of his “machinations,” and his elitism.

“The idea that has bothered me most is that he was the elitist and Jefferson was the democrat,” Ms. Berkin, who is a professor at Baruch College and the Graduate Center at CUNY, said. Hamilton was a certain type of elitist, Ms. Berkin acknowledged: He believed in meritocracy — one of the reasons he opposed slavery was that it wasted human potential — and he believed that those who had proved their talent and intelligence should be allowed to run the country.

“He was not an elitist in the sense of ‘I was born higher than you, therefore I am better than you, and I deserve more,'” Ms. Berkin said. “That was Jefferson.”

The film is just as poignant on Hamilton’s downfall as on his beginnings. When Washington died in 1799, Hamilton lost his great supporter, and he increasingly made disastrous political decisions. The next year, for instance, he wrote a pamphlet attacking John Adams, who was running for re-election; it resulted in the election of Jefferson and the collapse of Hamilton’s own Federalist Party. In 1804, when Aaron Burr was running for governor of New York, Hamilton attacked him viciously, provoking Burr to challenge him to a duel. Even though his beloved eldest son, Philip, had recently died in a duel, Hamilton accepted.

In the film, Mr. Chernow, the author of recent biography of Hamilton, draws a line from Hamilton’s birth to his death, arguing that illegitimacy “produced in Hamilton a lifelong obsession with honor.” Because of his religious beliefs, Hamilton didn’t even fire at Burr.

Founded in 1994 by Richard Gilder, who is an investor in this newspaper, and Lewis Lehrman, the Gilder Lehrman Institute has created history-centered public schools, organized seminars and enrichment programs for teachers, sponsored lectures by historians, and produced publications and traveling exhibitions. It also administers the Gilder Lehrman Collection of more than 60,000 documents on deposit at the New-York Historical Society.