Type of Book

[Russy]

What is a book containing various literary compositions called ?

[kempie]

Compendium?

[shaneystar]

A collection of literary pieces, such as poems, short stories, or plays is called an anthology.

[kempie]

Depends on the context of 'various'.

Anthology is normally applied to various collections of  works suggesting a common theme, whereas compendium is a compilation of a variety of works.

[Postumus]

Medley covers most of the possibilities