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Copyright is designed to give authors an incentive to create original works by affording them a limited-term monopoly on their intellectual creations.
Copyright is best understood as a suite of five rights:
The right to reproduce your work
The right to distribute your work
The right to display your work
The right to perform your work
A work is in the public domain if:
It is no longer under copyright (e.g. the term has expired, it has not been properly renewed)
It does not meet the requirements for copyright protection (ideas, procedures, methods, etc.)
The author elected to put the work into the public domain (many works with the Creative Commons license fall into this category)
It is a work of the United States government (may exclude the work of independent contractors)
Once a work falls into the public domain, it is no longer copyrightable and anyone may use public domain works without the permission of the copyright holder, who is no longer entitled to the exclusive rights of a copyright holder. These works can be excellent choices for use in teaching and research because there are no permissions required for their use.
Determining whether or not a specific work has fallen into the public domain can be difficult, this Digital Copyright Slider can help. Other sources for public domain material and research on the public domain: