Unless they are very short, two independent clauses joined by a coordinate conjunction ("and," "but," "for," "nor," "or," "so," "yet") are separated by a comma:
Criticisms of Shakespeare's plays fill whole libraries, but the facts of his working career can be summarized in a brief pamphlet.Two independent clauses not connected by a coordinate conjunction are separated by a semicolon, unless they are members of a longer series of such clauses. Compare these two sentences:
Criticisms of Shakespeare's plays fill whole libraries; the facts of his working career can be summarized in a brief pamphlet.
Criticisms of Shakespeare's plays fill whole libraries, the facts of his working career can be summarized in a brief pamphlet.The first clearly presents two independent and equally important ideas; the reader sees immediately that they are to be contrasted. The second version (a "run-on sentence" or "comma splice") is initially confusing. Seeing the comma, the reader thinks a third element will follow in the series, like this:
Criticisms of Shakespeare's plays fill whole libraries, the facts of his working career can be summarized in a brief pamphlet, but the details of his married life need only a single paragraph.Readers of the second version eventually can see what is meant (and they will also see that it is incorrectly punctuated), but it is your business as a writer to make understanding prompt, not eventual. Do not overuse the semicolon, but remember that it is an important signal to the reader, indicating that a following clause is a fully independent addition to or modification of what precedes it.