With documentary features continuing to gain ground as mainstream entertainment — lots of people are showing up for “Won’t You Be My Neighbor?” and “RBG” — their subject matters are becoming more intriguing and, in many cases, more peculiar. “Three Identical Strangers,” a darling at this year’s Sundance and Hot Docs International Documentary Festivals, clicks on both counts.

The opening sights and sounds are of 56-year-old Bobby Shafran, sitting down, looking into the camera, and saying, “When I tell people my story, they don’t believe it ... but it’s true, every word of it.” Then he calmly launches into that story, explaining that it really began when he was 19 and a freshman at Sullivan County Community College, where other students joyfully greeted him, many of them saying, “Welcome back, Eddy!”

“What? But I’ve never been here before,” remembers Bobby. And, by the way, “My name is Bobby. Who’s Eddy?”

Even after so much time has gone by, Bobby is still incredulous about the events that followed. The film shows some of them in a series of imaginatively presented old-style “flashbacks” that are actually color-saturated recreations of what went down.

But speaking as a movie fan and audience member rather than a critic this time, I’m only going to reveal a small amount of what happens in this film. The main reason is that I was so caught off guard right at the start and then again by the journey I was taken on as I sat there, open-mouthed and, on a couple of occasions, yelling at the screen, “No way!” or, using Bobby’s word, “What?”

My hopes are that your experience of watching this will be at least close to mine. I knew nothing about it, and I’m going to share only a little more here.

Those college kids weren’t completely wrong; th