1.a. In the event that: -- If I were to go, I would be late.
b. Granting that: -- If that is true, what should we do?
c. On the condition that: -- She will play the piano only if she is paid.
2. Although possibly; even though: -- It is a handsome if useless trinket.
3. Whether: -- Ask if he plans to come to the meeting.
4. Used to introduce an exclamatory clause, indicating a wish: -- If they had only come earlier!