Addendum:
Consideration of modes can take two aproaches.
1) as above, the 'parent scale' method. I.e. You derive Eb Lydian from Bb Major.
2) by considering alterations to the scale, one can derive similar results. I.e. You may derive Eb Lydian by raising the 4th note a half-step.
This shows the modes of C Major, with the relative key signatures to demonstrate the alterations.
For some it's easier to remember Aeolian = 6th mode; for others, to recall that Aeolian = b3, b6, b7. To each his own. I find the first method to be more intuitive for realtime improvisation.