Egg white contains albumen which has a strong adhesive power. It was used for centuries as a binder in tempera, for book illumination and for gilding.
To make the glue, beat the egg white, mix with water and let settle one night before use.
To glue paper, there are recipes where beaten egg white is mixed with ground egg shells to a paste.
This glue does not keep.
The adhesive properties of egg whites are used in the kitchen: it binds salt in the crust over meat or fish, or sugar in cake coverings.