While Barnard does have books about music and many videos of musicals/operas, our friends across the street at Columbia's Music & Arts Library (7th floor of Dodge) have a massive collection of books, sheet music/scores, and sound recordings on CD, in addition to a digital music lab.
Photo of Gabe M. Wiener Music & Arts Library, courtesy Columbia Libraries
Books and sheet music are lent out for a semester at a time, while recordings are available to be checked out for 4 weeks at a time.
Columbia's Music Library also hosts a series of free (for students and faculty) Music Technology Workshops each semester. Examples of Spring 2019 workshop topics include Ableton Live, digital sampling, guerrilla recording techniques, digital signal processing, mixing workshops, and more.
For other guides in the performing arts, see the links below:
Some of these online encyclopedias and reference sources may be good starting-points for research!