"Above all learn to breath correctly"
In Pilates we have a specific way of breathing, that may be difficult to understand at first especially if you come from different sports or disciplines.
Think about your core as a cylinder, with a top and bottom, a right and left, a front and a back.
As Pilates focus on strength and stability, belly breathing isn't possible. We therefore prefer to breath laterally into the ribs as well as the back of the body. This way we have our oxygen supply and we can maintain the abdominal engagement for the most challenging exercises.
Even though breathing is important, don't let "the correct way" to breath stop you. Breathe in and out as it feels logical and natural to you and, most certainly if your core is engaged your breathing is correct.