When extended an invitation can I bring a guest?

Sometimes. On a mailed invitation, if you are invited to bring a guest, the envelope will either say "John Doe & Guest" or the host will enclose a note notifying you that you can bring a date. In a more informal event, it depends on the method of invitation and type of event. Check with the host if you are unsure.

If a mailed invitation is addressed to you and no guest is mentioned, you are invited alone.