I
Ionian mode - a diatonic major scale beginning with the same note as the key signature followed by a tone, tone, semitone, tone, tone, tone and semitone to the octave.
inversion - usually a triad chord formation that does not have the root as the lowest note. The first inversion would begin with the third, then the fifth, then the root at the top. The second inversion would begin with the fifth, then the root, then the third at the top. A third inversion would involve a chord with an added harmony such as a sixth, seventh or ninth, etc.
improvise - improvisation is a spontaneous, musical performance created by using variations of the melody rather than the melody itself. A deep understanding or sense of harmony, mode, rhythm and timing are required to solo over even the simplest progressions.
intervals - the number of steps between two notes, usually beginning with the root (Do, as in Do, Re, Mi). From Do to Re is called a second. From Do to Mi is a third. From Do to a flatted Mi is a minor third. From Do to Fa is a fourth, Do to a flatted Sol is a diminished fifth, Do to Sol is a fifth, Do to a sharp Sol is an augmented fifth, Do to La is a sixth, Do to a flatted Ti is a seventh, Do to Ti is a major seventh, Do to Do is an octave, and Do to a flatted Re is a flat ninth.