An uncertainty, possibility, condition, doubt etc.
Supposing that, assuming that, in the circumstances that; used to introduce a condition or choice.
If it rains, I shall get wet.
In the event that a statement is true (a programming statement that acts in a similar manner).
If A, then B, else C.
Supposing that; used with past or past perfect subjunctive indicating that the condition is closed.
I would be unhappy if you had not talked with me yesterday.
Supposing that; given that; supposing it is the case that.
If that's true, we had better get moving!
Although; used to introduce a concession.
He was a great friend, if a little stingy at the bar.
(sometimes proscribed) Whether; used to introduce a noun clause, an indirect question, that functions as the direct object of certain verbs.
I don't know if I want to go or not.
(usually hyperbolic) Even if; even in the circumstances that.
Introducing a relevance conditional.
I have leftover cake if you want some.