As an introductory phrase, use a comma after "in contrast" or "by contrast" to show a clear difference between two o more things.

Use commas to set off parenthetic expressions and nonessential words, phrases, or clauses. Do not use commas to separate essential or restrictive information.

Generally, we should add a comma after an introductory phrase. The comma, however, may not be necessary if the introductory phrase begins with a preposition, or it is very clear and brief (no more than three or four words).

Do not join two complete sentences with a comma (also called comma splice). You can fix it by adding a semicolon, placing a period, or using a conjunction.

If each element of a numbered or bulleted list is a complete sentence, capitalize the first word and place a period at the end. If the elements of the list are single words or phrases, capitalization and punctuation marks (including commas) are optional.

In a list of three or more elements, add a comma after each element except the last.

Use a comma before a coordinating conjunction or a correlative conjunction to separate two independent clauses.

When two independent clauses are joined by a correlative conjunction, use a comma to separate them.

Frequently, no comma is necessary when using "rather" or "rather...than". However, there are particular sentence structures where commas are required.