One very common injury among tennis players, primarily older, is the displacing or injuring of the Rotator Cuff. Your Rotator Cuff is located at the top of your shoulder, which makes it a spot that gets worked a lot while you play. Hurting your Rotator Cuff can result, depending on the magnitude, in not being able to play for vast extents of time, even never being able to play again, if you are a senior player. Fortunately, there are a few great exercises that will not only prevent that area from being harmed, but will strengthen your stroke as well.

Exercise Number 1 - You will need dumbells with light weight on them, whatever your comfortable with.
1) Lie down on your side.
2) Grab the dumbell as if you were doing a tricep curl. (Forearm should be facing you)
3) Lift it from that grip up to your shoulder and then back down
4) Do two sets of 10 on either side.

Exercise Number 2 - Nearly identical to the first.
1) Repeat Step one of the first exercise.
2) Grab the dumbell as if you were doing a BICEP curl. (Forearm will NOT be facing you)
3) Repeat the last two steps of exercise 1.

Exercise Number 3 - You will need dumbells again.
1) Stand up straight, holding a dumbell in each hand with a neutral grip.
2) Make the motion as if you were swinging your arms out, with the dumbells in hand.
3) When you swing your arms out, rotate your wrist so that your forearm goes from facing away from you to facing toward you.
4) Do 2 sets of 10.

If you do these exercises three or four times a week, you will have a safe and healthy Rotator Cuff, and you will find your strokes getting stronger and faster.