(Just a little handmade rubric to know which routes are which.)
Routes
Route 1 (New Moon - Sunrise)
Route 2 (New Moon - Sunset)
Route 3 (Twilight Forest - Dusk City)
Route 4 (Dusk City - Crescent Town)
Route 5 (Dusk City - Asteroid Valley Entrance)
Route 6 (Asteroid Valley Exit- Dawn City)
Route 7 (Dawn City - Sola Town) (Can take train to avoid desert)
Route 8 (Dawn City - Nova Town) (Can take train to avoid desert)
Route 9/Stardust Bridge (Luna Mountain Town - Stardust City) (Can surf under the bridge)
Route 10 (Luna Mountain Town - Astral City) (Can use boat instead of surfing)
Route 11 (Astral City - Full Moon City)
Route 12 (Full Moon City - Victory Road Entrance)
Route 13 (Victory Road Exit - Battle Island) (Must have surf)
Route 14 (Battle Island - Elestia Pokemon League) (Can request ferry service instead of surfing)
Route 15 (Eclipse Forest Exit - Crescent Lake)
Mountains
Mountain Route 1 (Dusk City - Luna Mountain Town)
Mountain Route 2 (Dawn City - Stardust City) (Can take train to avoid mountains)
Mountain Route 3 (Nova Town - Meteor Plains)