There are many who consider the colon and semi-colon to be identical punctuation stop marks and use both without discrimination, while others have a strong preference for one mark and have little use for the other. Here I am going to concentrate solely on the use of colons.
The colon is described in the New Oxford Style Manual (2012 edition, p. 73) as follows:
“The colon points forward: from a premise to a conclusion, from a cause to an effect, from an introduction to a main point, from a general statement to an example.”
Notice that I prefaced the quotation with a colon, as an introduction to what is to follow. It fulfils the same function as introductory phrases such as for example, for instance, because, as follows, and therefore. Text that follows a colon need not contain a verb or be a grammatically complete sentence that can stand on its own from the preceding material. From the above you would also notice that colons can introduce speech or quotations.
Some examples of using a colon to introduce the following text are:
The cardigans are available in three sizes: small, medium and large.
The cotton napkins are available in two colours: white and cream.
Colons can also be used to introduce lists, as in:
The shoe box contained all manner of mementoes of her life as a teenager: school reports, diaries, concert tickets, holiday snapshots and love letters from her first serious boyfriend.
But it would not be correct to say:
The article cited three authors:
namely Smith, Jones, and Williams
as “namely” links to words in the text introducing the list, so you should say:
The article cited three authors, namely, Smith, Jones, and Williams
Colons can also be found in book, chapter, and text headings to separate the main heading from the sub-heading and can be widely seen in the formatting of reference and bibliography sections of books (for instance, in citing journal issue data).
Notes on usage: in British English the word immediately following a colon is not capitalized unless it is a proper noun, but in American English it is generally capitalized if it introduces a grammatically complete sentence. Also, it is now considered old-fashioned to follow a colon with a hyphen or dash and should be avoided unless reproducing text in antique or foreign-language typography.