Core Training for Athletes
The core is essential in stabilizing the body in almost all movements, including sprinting and vertical jump. That means if you want to jump higher or run faster, you have to gain core stability. That doesnt mean you need to do a thousand situps a day,which is the wrong method anyway, trying to get a six pack. So instead of situps and crunches (although crunches can serve some purpose), pick exercises that require the core to stabilize the body, such as overhead squats or woodchoppers.
Anatomy of the Core
The rectus abdominus is found between the ribs and pubic bone. This is the muscle that forms the "six pack". Its purpose is to move the body between the rib cage and the hip. Most athletes make the mistake of training this muscle without focusing on other abdominal muscles.
The external obliques are found on both sides of the rectus abdominus. They contract when you twist your trunk, so are extremely important when doing 180 or 360 dunk.When you twist to the right, the left external oblique contracts; when you twist to the right, the left contracts
The internal obliques are found just inside the hip bone, and also allow the body to twist.
These are the opposite of external obliques because when twist to the left the left internal oblique contracts and vice versa.
The transversus abdominus is the deepest muscle layer in the abdomen. Its main purposes are to keep the pressurethe of organs in the body normal (which prevents hernia) and to stabilize the abdomen.
Reccomended workouts for the core
Overhead Squats- I like these because they kill two birds with one stone. You are squatting, which works your quads and posterior chain, and the core is also forced to stabilize your body.
Lunges- This is also a multiple muscle exercise. It hits the quads hard, and if you keep a straight spine (which you should) while performing the rectus abdominus will also be used to stabilize the body.
Twists- Great for the obliques, IMO better than side bends. You can also add these to almost any exercise. After every rep you can perform a twist which wil give you more time to focus on other things. Its called training economy 
Woodchoppers- Possibly the best core stabilization exercise out there. Easy to do, great for overall athletic performance.
Leg Raises- not great for vertical jump but good for isolating the lower rectus abdominus.
Pushups- another multiple muscle exercise. With as many variations you can perform, you can hit almost every muscle in your upper body along with the core.
Swiss ball hip extensions- works the hip flexors and the abs.
There you go. Probably not that good compared to everything else on here, but i thought i would share some knowledge anyway.
