The Fair Use provisions of the Copyright Act of 1976 (Section 107 of the U.S. copyright law) allow certain uses of a work without prior contact with (or payment to) the copyright holder. Note that many, but not all, academic uses come under this heading.
Congress provided the criteria for whether Fair Use applies to one's use of a copyrighted work, and is determined by the cumulative assessment of these four factors:
1. The purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes.
(The Transformative Factor):
2. The nature of the copyrighted work
3. The amount and substantiality of the portion used in relation to the copyrighted work as a whole.
4. The effect of the use upon the potential market for or value of the copyrighted work.
Fair Use is a complex topic, and there are few hard-and-fast rules about exactly how much of a copyrighted work can be reproduced without obtaining explicit permission. Indeed, the concept of Fair Use hinges on the idea that permission is not needed provided scholars do the following:
(From: TriCo's Music Example Guide)