I really enjoy and specialize in teaching the short game. Without a doubt it is the most overlooked aspect of the game. A golfer can make up for a lot of full-shot mistakes with a solid game from 100 yards in. Pitching, chipping and putting are a strong part of every good players game.
Other aspects of golf I've studied are course management and the psychology of scoring. These are subjects that often come up during a lesson and are likely to be discussed. The best place to focus on these aspects is on the course with a playing lesson.