1. Reading jazz chord symbols
Jazz symbols compress a lot of information. Cmaj7 means C-E-G-B. Cm7 means C-E♭-G-B♭. C7 means C-E-G-B♭ and often functions as a dominant chord. Cø7 means C half-diminished seventh: C-E♭-G♭-B♭.
2. Extensions: 9ths, 11ths, and 13ths
Extensions continue stacking thirds above the seventh. The 9th is the same letter as the 2nd but placed above the octave. The 11th relates to the 4th, and the 13th relates to the 6th. These notes add color.
3. Altered tones
Alterations modify extensions, especially over dominant chords. You may see C7♭9, C7♯9, C7♯11, or C13♭9. These create tension that usually resolves to another chord.
4. Shell voicings and practical piano use
A pianist does not always play every note in a jazz chord. A shell voicing often uses the root, third, and seventh because those notes identify the chord function clearly. More advanced voicings may omit the root if a bass player is present.