The muscles that make up the core include:
THE BACK:
multifidi (deep, small local muscles passing along 2-3 spinal segments); erector spinae (large muscle group extending the length of spine); quadratus lumborum (deep, side flexor of the spine)
THE ABDOMINALS:
transversus abdominis (the deepest and the first abdominal muscle to contract and support the spine before limb movement occurs link);
internal obliques (deep muscle, aids in trunk rotation and side bending)
external obliques (most superficial abdominal muscle);
rectus abdominis (the most prominent and well-known 'ab' muscle).
THE HIPS:
gluteus maximus and medius (have an important role in transferring force from the legs to the spine.)
Weak hips have been associated with increased knee injuries. link