Caught Foul Ball: Out or Strike? Understanding Baseball Rules

Question
If a batted ball that goes upward and does not go above batter's head and is caught by the catcher either fair or foul, an out or just a foul ball that is a strike on the batter, and if runners on base can they advance?

Answer
What you have is a caught fly ball regardless if the ball is caught over fair or foul terriorty.  Whether or not the ball goes above the batters head has no affect on anything, ever.   This is an out and the runners may advance as long as they don't leave the base prior to the catch.

Tom