Music theory is a strange child in music education. Many teachers ignore her, yet she is basic to everything in music. The basic ideas in music theory can be taught to a kindergartner, yet music majors and minors sit in college classes learning music theory that no one taught them for the last ten years while they were learning their instruments in grade school.
Fundamentals of music theory for all musicians:
Order of sharps and flats
Write all major and minor scales and play them on your instrument.
Read time values of notes and rests.
Identify time and key signatures
Know the meanings of tempo markings (i.e. allegro, andante, largo etc.)
Know the meaning of dynamic markings (pp, p, mp, mf, f, ff)
Know how to write basic major triads I, IV, V7 in any key.