Stance is the first golf fundamental taught. The stance includes the approach to the ball and body positioning. This is important because a bad stance causes bad shots. The idea is to feel comfortable when approaching the ball.
There are three primary grips: baseball, interlocking and the Vardon (sometimes called overlapping) grip. While it's not important which grip is used, instructors will teach the aspiring golfer to grip the club properly and how to swing it given the grip that is used.
There is no question the swing is the No. 1 factor. Everything from the backswing to the downswing is emphasized.
Strategy is taught so the golfer can take action on the ball depending on where it lands. Areas of emphasis are where to hit the ball (primarily if it is an errant shot) and how to hit the ball out of tough areas.
Part of learning golf is learning about shot selection. In golf school, you are taught to determine where you are on the hole and which club is best used to get your ball closer to the hole.