Music theory is the scientific study of sound and music and is a systematic understanding of how music works. Reading music or notation is a component of theory and is the symbolic representation of music.

A musician who understands theory can learn any instrument once they understand how the instrument physically works, because sound and music is universal across instruments. For this reason most musicians will tend to use the piano to explain and examine theory. Indeed, learning theory on the piano means that you will literally be 'reading' the piano. 

Reading or music notation will be essential to most serious musicians at some point. It is not as important as the perception skills - pitch or rhythm, but then pitch and rhythm can be better understood by learning to read. Many young musicians appear to be reading music as they play and look at a score, but from what we see they are often not genuinely reading but using a hybrid method of following the notes and playing from memory. The reason for this is they tend to learn the easy part of notation - the name of the notes. The difficult part is the rhythm of the notes. We use advanced methods including computer software to train music rhythm reading. This not only helps develop reading but will also help with rhythm in general.