Lydia Cohen was picking classes for her last semester at New York University when she saw it: an entire class about Taylor Swift.

“I was like, ‘Oh, my God, I need to get into this class,’ ” said Ms. Cohen, a devoted fan of the musician who listens to her songs as soon as she wakes up. “How does this exist?”

For nearly two months, the 22-year-old media-culture-and-communication major joined 19 other NYU students for 2.5 hours every Wednesday night to study the superstar. They discussed her impact on the music industry, her songwriting style, her feud with rapper Kanye West and whether Jake Gyllenhaal has her scarf.