Glossary
Apparent Magnitdue, Absolute Magnitude & Distance Modulus

These are measures of the brightest of an object, and based on the original classification scheme used by Hipparchus of Rhodes who assigned an apparent magnitide m = 1 to the brightest stars in the sky (excl the Sun), and an apparent magnitide m = 6 to the faintest stars visible to the naked eye.

The scheme has since been formalized on a logarithmic scale such that a difference in apparent magnitude m1 - m2 = 5 corresponds to a difference is brighness of exactly 100. ie
log10 (F2/F1) = 2 (m1 - m2) /5
brighter objects have lower apparent magnitudes

The luminosity (assuming isotropic emission) of something a distance r away observed with a flux F1 is obviously
L1 = 4 pi r2 F1

Again for historical reasons, the absolute magnitude is defined as
the apparent magnitude the object would have if it were at a distance r = 10 pc
more luminous objects have lower absolute magnitudes

The relation between an object's apparent magnitude (m) and apparent magnitude (M) is obviously related to its distance in parsecs
log10 (F2/F1) = 2 log10 ( d / 10)
so
m - M = 5 log10 (d) - 5 = 5 log10 (d / 10 pc)
This is known as the Distance Modulus