A really beautiful library that provides a quiet environment for working or studying, surrounded by great views. There are very many seating options spread out across the 8 floors. There are power outlets everywhere and plenty of restrooms. The only downside is that there is no visitor WiFi. Only university students can access the WiFi, which is a shame. So as a visitor you'll have to use your own wireless hot spot.
The nearest MRT station is Taipei Zoo, but it's a 25 minute walk away. Instead, if you're coming from central Taipei, it is probably better to just catch a bus, of which many stop just outside the university. Anyone can access the library, although you'll have to sign-in on the computer when you arrive and hand in your ID card to the reception staff in exchange for a temporary access card.