Stability balls are great for core training: they require your muscles to work much harder than they would on a stable surface, and in turn you get a better workout in a shorter amount of time. I also like them for my personal training clients who have lower back issues because the ball does not put the same type of pressure on the spine that mat work on the floor can. Stability balls come in several sizes, and you’ll want to choose which on to use based on your height. If you are under 5’7 you’ll generally want to use a 55cm ball. If you are over 6’2 you’ll want the 75cm ball. In between those heights a 65cm is usually best.
Check out this video for a short, but effective ab circuit:
Complete the circuit 2-4 times
8-15 ball passes
20-40 crunches or one leg crunches
20-20 mountain climbers on ball or maximum plank