Core Strength Yoga is an approach to hatha yoga that emphasises the importance of using the inner body to support the outer body. This means developing awareness of core muscles, including the pelvic floor, the
transverse abdominus and the deep back postural muscle, multifidus. 
Awareness of, and work on, the iliopsoas and other abdominal muscles
is also important in developing a strong sense of core around which a
stable and aligned posture can be held.  In hatha yoga, core muscles
should be strengthened and used to stabilise the centre of the body
so that students are supported from within when they are doing asanas. 
Core Strength Yoga is suitable for all abilities and everyone benefits from
working with core muscles.  Posture improves, students are less prone to
back pain and the structure of the body comes into better alignment around gravity. My approach to what I call Core Strength Yoga is influenced by
my own experience of working with bandhas (energy seals or locks) in
Ashtanga Yoga. I found myself bringing a lot of that work into my general,
much more gentle, hatha yoga classes.  I have also been influenced by the
work of Tom Myers in his book, Anatomy Trains.  The whole Rolfing view
of the body as a tensegrity structure is fascinating and very relevant to yoga practice.  I should pay tribute to my anatomy teacher, David Keil, for
inspiring me down this path.  His website is always worth a look at www.yoganatomy.com