A complex most visitors walk straight past
Just a few minutes from Charles Bridge, the Clementinum (Klementinum) is easy to miss entirely — its plain Baroque facade gives little away about what's inside. It began as a Jesuit college in 1556, grew over the following two centuries into the second-largest historic building complex in Prague after the castle itself, and today houses the National Library of the Czech Republic.
The Baroque Library Hall
The reason to visit is the Baroque Library Hall, routinely ranked among the most beautiful libraries in the world — a single long room lined floor to ceiling with historic volumes, its ceiling covered in elaborate fresco work, and antique globes standing among the shelves. It's a working part of the National Library's historic collection, which is exactly why you can't simply wander in: entry is by guided tour only, in small groups, on a fixed route through a handful of the complex's most significant rooms.
The Astronomical Tower
The same tour typically includes the Astronomical Tower, used historically for real astronomical observation and as the meridian reference point for official Prague time in past centuries — a cannon at the castle was once fired daily based on a signal from here. Climbing it today gives one of the better rooftop views over the Old Town, arguably less crowded than the castle-hill viewpoints covered elsewhere on this site.
The Mirror Chapel
Depending on the tour route, you may also see the Mirror Chapel, an ornate Baroque chapel that doubles as a concert venue — if classical music is part of your trip, a concert here is worth checking for specifically, since the setting does a lot of the work.
Practical notes
Tours run on a fixed schedule with limited group sizes, so this is one of the few sights on this site worth booking ahead rather than turning up on spec, especially in peak season. Photography rules inside the library hall are stricter than at most Prague sights — expect this to be enforced, since it's a working library collection, not a museum reproduction.