The Importance of the Knees in Tennis:

What is the role of the knees in tennis?
The muscles of the knee generate the power for your strokes, control your balance, and provide you with vertical power. The principle muscles are the quadriceps (front of the thigh) and the hamstring group (back of the thigh).

How should you strengthen them to improve your game?
To strengthen these muscles, you need to do knee squats (halfway only) and knee curls. follow these guidelines for strength training in the ACSM guidelines.

What are the most common injuries?
The most common injury is a hamstring pull. An imbalance in strength is known to put you at risk for hamstring problems. The ideal strength ratio is 60 (quadriceps) : 40 (hamstrings). Thus if your maximum strength for the quadriceps is 60 pounds, then the maximum strength of the hamstrings ought to be 40 pounds. In addition to developing strength, you ought to be training to develop these strength ratios. If you do develop a hamstring tear, rest is usually prescribed followed by gradually returning to strength training.