I’ve seen “Hamilton” four times.

Well, maybe more like 3.33 times. (More on that later.) But with all the media hype, the 11 Tony Awards, the tickets selling for thousands of dollars on the secondary market and the fans camping out overnight, everyone I meet is desperate to see “Hamilton” just once. Because of my job, I’ve seen it multiple times over the last year and a half. Here’s what it’s been like.

THE FIRST TIME

By the time I first saw “Hamilton” I’d been hearing about it for years, because in the theater industry, “Hamilton” was big before it was big.

Sure, I’d seen the YouTube clip of Lin-Manuel Miranda at the White House in 2009, performing an early version of the rap that would become the opening number of the musical. But the first time I remember having my head turned by the buzz was soon after the spring 2014 developmental workshop of the show, when a commercial producer who’d seen it — one of the sanest, most clear-eyed producers out there — talked up the show like it was a life-changing event. Six months later, a significant player in the development of the production, one with a long and influential resume, told me “Hamilton” might be the best thing he’s ever worked on.

These were pretty jaw-dropping endorsements, but I took them with a grain of salt. Industry buzz had once been pretty enthusiastic about “Bullets Over Broadway,” and that one didn’t even last six months.

Like most people in the press, I finally got the chance to see what everyone was talking about at one of the preview performances, just a few days before the production premiered in a 299-seat auditorium at Off Broadway’s Public Theater on Feb. 17, 2015. Those two producers weren’t kidding: The show was thrilling, a vivid, propulsive, and contemporary retelling of bone-dry American history organized around the single genius impulse to link the raucous rumblings of a new nation with the swagger, pugnaciousness and ingenuity of today’s hip hop culture.

The first act was electrifying. The biggest surprise came for me in “Satisfied,” the song immediately following Hamilton’s marriage to his wife Eliza. Out of nowhere, Eliza’s sister Angelica (Renee Elise Goldsberry, who deserves every ounce of the Tony she won for her performance) takes center stage and winds time backwards, revealing her own love for Hamilton, enumerating the reasons she suppressed it, and making everyone in the audience fall madly in love with her.

Thanks to that preview performance, I’m one of the few people to see Brian d’Arcy James, the always-excellent Broadway regular of whom movie audiences finally took note in “Spotlight,” play King George III. D’Arcy James originated the royal role, but left the Public production on March 1, 2015 to take the lead in Broadway’s “Something Rotten!” (ceding the throne to the Tony-nominated Jonathan Groff). His performance was the other highlight of that initial viewing of “Hamilton” for me, in part because it was the first time I’d heard the hilarious, razor-sharp, Beatles-esque breakup tune “You’ll Be Back,” and in part because d’Arcy James, who’s got the best deadpan in the business, underplayed it with just the tiniest glint of steely derangement. (Groff and his replacement, Rory O’Malley, are great too! But I’ll always love my first time.)

Early in the second act, I remember thinking that, for a brief stretch, the show’s inspiration had flagged. But only briefly, and it didn’t matter by the time “It’s Quiet Uptown,” a song about the reconciliation between Hamilton and Eliza after a couple of marriage-shattering events, turned the show into an unexpectedly moving experience.

I came out loving “Hamilton,” and even before the rave reviews hit, it was a sure thing for Broadway. But I never thought it would break through into pop culture like it has, because musical theater doesn’t do that. Or at least it hadn’t in a very long while.

THE SECOND TIME

The second time I saw “Hamilton” was its Broadway opening on Aug. 6, 2015, and by that point, it was a thing. Critics had gone gaga. Celebs had clawed for tickets to performances in its small Off Broadway home. Madonna ended up in gossip columns for texting during the show. There was a moment when it looked like the production was going race into a Broadway slot prior to the cutoff for the 2014-15 Tony Awards. By the time the production ended up at the Richard Rodgers Theater as part of the 2015-16 season, it was already considered the presumptive champion of the 2016 Tony Awards.

I can’t actually tell you what changed in the show between February and August, and the musical’s running time barely shortened. But there was clearly some honing done, particularly in the second act, which felt fleeter, leaner and smoother. And it looked great in the Rodgers, one of Broadway’s best houses to sit in.

With no need to stress over what the critics would say the next morning, that opening was like a big, supportive party for everyone involved in the show. (I sat next to Robert Greenblatt, the NBC Entertainment chair who’s an investor in the show.) Most Broadway after parties are frugal affairs, but this one — held at the Lighthouse, the Chelsea Piers venue that hosts some of Broadway’s swankest opening nights — culminated in actual fireworks over the Hudson River.

It was around then that I started to understand the impact of “Hamilton.” Usually when I tell people what I do for a living, the standard response is, “What should I go see?” By fall, it had become “What do you think of ‘Hamilton’?” Or, if you’re pushy, “Can you get me tickets to ‘Hamilton’?” (Folks, I’m not sure I can get my own mother tickets to “Hamilton.”)

THE THIRD TIME

I didn’t see the show again until May, and by then, the “Hamilton” fatigue was real. The hype, the media coverage, the broad-spectrum fervor — it was all a great thing for musical theater, in terms of imbuing the form with a hip factor it hadn’t had since “Rent,” and in getting new, younger audiences excited about theater. But if I had to read another article about “Hamilton” (or write one), I’d lose my mind.

So when I sat in on one of the show’s series of student matinees, performed monthly for audiences made up entirely of NYC high school students who have paid $10 each for a ticket, I came in a little jaundiced.

I sat in one of the loges, in a seat that had a very obstructed view of stage left, but that didn’t matter. I was there to watch the kids. And their response reminded me that the show actually is as exciting as everybody says it is.

The students cheered for the actors like they were rock stars. They were noisy, but in the most attentive, responsive way. Of course they went wild every time there was kissing or romance or a hint of sex, but they were caught up in the story enough that when Hamilton’s adulterous gettin’-busy R&B tune “Say No to This” rolled around, they very clearly disapproved of him cheating on his wife. They gasped at the violence of war implied in the choreography. Probably most amazingly, they cheered and hooted every time Hamilton landed a verbal jab in a rap battle over, of all things, the creation of the Federal Reserve. These kids were into it.

The third viewing also reminded me why the score to the show has become one of the rare Broadway cast albums to cross over to the contemporary music charts: Because it’s really, really catchy.

THE FOURTH TIME

I haven’t sat all the way through “Hamilton” for a fourth time. But as a reporter covering the hullaballoo around the final performance of Miranda (and of two of his co-stars, Leslie Odom, Jr. and Phillipa Soo) July 9, I had the chance to get walked in for the curtain call.

I ended up seeing the last 45 minutes or hour of the show that night, standing at the back of the Richard Rodgers Theater. (I came in right around when Hamilton decides to write the Reynolds Pamphlet.)

The engaged excitement of the crowd was palpable, the laughter quick and enthusiastic, and, toward the end, the crying audible and omnipresent. This was an audience savoring every minute, and the same seemed true of the actors. Soo went at her song “Burn” with even more intensity and heartbreak than usual, and Miranda seemed to feel every moment with new immediacy.

It was pretty moving, and it served to remind me how surprised I had been at the show’s emotional power the first time I saw it. It goes a long way to explaining why the musical has proven as resonant as it has, even beyond the accessibility of its super-smart concept.

I also picked out more clearly than ever the influences that Miranda has always worn on his sleeve. I heard Sondheim in “Your Obedient Servant” (“Careful how you proceed, good man / Intemperate indeed, good man”), and recognized “Les Miserables” in the death of Hamilton’s son (which is the show’s own “and rain will make the flowers grow” moment).

I had spent the 90 minutes prior to the performance interviewing the ticket holders and fans who had turned up for the July 9 show, and it was impossible not to be heartened by the sheer volume of young people excited about theater. I suspect we’ll be seeing the ripple effect of that for years.

So to the people who beg me for details about “Hamilton,” I usually say: Yes, it’s great. Yes, you should see it, with any cast you can. And yes, there’s a decent chance I’ll end up seeing it again sometime.