1) To join two clauses of a compound sentence when there is no conjunction
He hadn't had his first cup of coffee yet; he wasn't ready to start work. (In this sentence the semicolon is close to a period in function. We can use a semicolon instead of a period to join two clauses that are closely related in idea. We could also put a comma and a conjunction between these clauses.)
2) To use with a conjunctive adverb
He wasn't ready for work; however, he knew that he had to finish the report before the day was over. (Conjunctive adverbs are words like " however," " therefore," " nevertheless," " consequently." When these words come between two independent clauses, they are preceded by a semicolon and followed by a comma.)
Words like " however," " therefore," etc. are conjunctive adverbs only when they come between two independent clauses. If they occur in the middle of a clause, they are preceded and followed by commas.
He hoped, however, that he would be able to slip out for coffee before his boss came in.
3) To separate elements that contain commas
He glanced at Joan Grimsby, the sales manager; Alan Gillespy, head of the accounting department; and Reggie Vanderbilt, the boss's fair-haired boy. (This sentence contains a series of names and titles with the names separated from the title by a comma.)
Click here for a semicolon quiz