Concentration. This is the most important principle in Pilates. You must be very mentally present as you do the exercises, aware of every aspect of your body's movement, alignment and muscle contractions.
Control. Every movement is done with control, so you aren't just throwing your body around. Centering. All exercises are done evenly using your entire body. Think of a plumb line down the middle of the body working both sides evenly. Fluidity. A smooth transition from one exercise to the next is important because once you've learned the routine; it should look something like a dance, where every movement flows into the next. Precision. You try to make each movement as precise as possible; alignment, placement of your limbs, position of each part of your body is paramount and a central aspect of how and why Joseph Pilates designed this system of exercise. Breath. How you breathe is very important in Pilates exercises. You don't want to hold your breath at all. Deep, steady breaths will help you maintain concentration and precision, too.