Ellipsis

An ellipsis is a series of periods with a space before each and a space after the last. ( . . . )

In prose (MLA and APA):
Purpose:  Used in a quote to omit material from the original sentence or sentences. 

Examples:
1. Use three periods when omitting part of a sentence: 

"Medical thinking . . . stressed air as the communicator of disease, ignoring sanitation or visible carriers."

2. Use four periods when omitting material after a completed sentence or between two sentences (Note: there are no spaces before the first period or after the last in this case):

"Medical thinking, trapped in the theory of astral influences, stressed air as the communicator of disease. . . ."

3. If the author quoted uses ellipsis points, place brackets around your ellipses to distinguish them from those of the author:

"We live in California, my husband and I, Los Angeles. . . [. . .]  I have never been here before."

In poetry (MLA):
Omitting words or phrases:  The ellipsis is used just as it is used in prose.

Omitting entire lines:  The ellipsis consists of a line of three spaced periods:
In Worcester, Massachusetts,
I went with Aunt Consuelo
to keep her dentist's appointment
. . .
It was winter. It got dark
early.

Sources: 

Gibaldi, Joseph. MLA Handbook for Writers of Reseach Papers. New York: The Modern Language Association of America, 2003.

Publication Manual of the American Psychological Association. Washington DC: American Psychological Association, 2001.