The mandolin, in standard tuning, is tuned like the violin: GDAE, or, in Helmholtz notation, gd'a'e''. (See https://en.wikipedia.org/wiki/Helmholtz_pitch_notation for an explanation of Helmholtz nomenclature.) I use alternate tunings, but I will address that later.
One thing I like about this tuning is its symmetry. A scale can be played in two halves, with each half using the same fingering. This is clearest playing a scale starting on an open string. The lower half of the G scale on the mandolin is fretted 0-2-4-5 on the G string, and the upper half uses the same frets on the D string. Fingering is open-1-2-3 on each string. The higher G scale is fretted 5 on the D and 0-2-3, then 5 on the A and 0-2-3 on the E. Fingering is 3-0-1-2 and 3-0-1-2.
Another aspect of this tuning is the ability to change keys by moving the fingers over a string or strings. Move that lower G scale over a string and you have a D scale. You can play the lower half of the higher-octave D scale as you would play the lower half of the upper G scale, but you must move up the fingerboard to third position to complete the scale, and I won't address positions yet. Move that same fingering over one more pair of strings and you have an A scale.
This holds true for scales starting on other frets, which I won't explain right now. It also holds true for arpeggios, or arpeggi. A G arpeggio is played 0-4 on the G string and 0-5 on the D. A D arpeggio is played 0-4 on the D and 0-5 on the A. Move that over one more set of strings for an A arpeggio.
Compare this to the guitar, where the fingering changes on every string, and you can see that this is one reason why melody works well on mandolin. Celtic tunes work well on mandolin also because the strings allow open strings to be played as drones along with the melody.
(When I use the singular "string" I refer to a pair of strings, otherwise called a "course".)