An Abridgment, Abridgement

1. (US) The act of abridging; reduction or deprivation [First attested from around (1350 to 1470).]

Synonyms: diminution, lessening, shortening[2]

2. (US) The state of being abridged or lessened.
3. (US) An epitome or compend, as of a book; a shortened or abridged form; an abbreviation. [First attested from around (1350 to 1470).][2]
4. (obsolete) That which abridges or cuts short; hence, an entertainment that makes the time pass quickly
5. (dated, law) Any of various brief statements of case law made before modern reporting of legal cases.
6. (law) The leaving out of certain portions of a plaintiff's demand, the writ still holding good for the remainder.

In current usage this spelling is about as common as abridgement in the US, but much less common in the UK.

Notes on near-synonyms:

An abridgment is made by omitting the less important parts of some larger work; as, an abridgment of a dictionary.

A compendium is a brief exhibition of a subject, or science, for common use; as, a compendium of American literature.

An epitome corresponds to a compendium, and gives briefly the most material points of a subject; as, an epitome of history.

An abstract is a brief statement of a thing in its main points.

A synopsis is a bird's-eye view of a subject, or work, in its several parts.

(act of abridging): compendium, epitome, abstract, synopsis, précis