Learn about the vast scope of Gyrotonic training by checking out the Exercise of the Week.
The Waterfall series on the Ladder or the Archway is the absolute best for pure front of the body core strengthening. While you're working the same muscles as a sit-up or crunch, you're asking your body to do the same thing in the opposite direction. The extra space you gain by being off the ground allows you to add fun variety, like Press Ups.
There are 6 ways you can move your spine. One of them, circumduction, is a circular movement of the spine, either internally or externally. The idea of this exercise is that its an internal circumduction if your spine was twice as long.
I recently recorded several exercises in the Levitation series and as I was selecting which exercises to use, I looked back at old syllabi to see if I was forgetting any really cool ones. I was. I haven't done Snake in years and I remembered how much I've always liked this.
While most of the exercises in the Hamstring Series focus on, well, the hamstrings, some exercises also let you get in a core workout. Keeping your pelvis floating off the bench while doing these small bicycles is a total body exercise that emphasizes core strength.