Here are all the classes known to the Angria Islands. Please keep in mind that you may only move to an upper-level class when you become experienced.
1st Class ~
Warrior
Magician
Archer
Thief
2nd Class ~
Warrior -> Knight or Gladiator
Magician -> Battle Mage or Acolyte
Archer -> Jester or Assasin
Thief -> Hunter or Ranger
3rd Class ~
Knight/Gladiator -> Paladin or Myrmidon
Battle Mage/Acolyte -> Oracle or Warmage
Jester/Assasin -> Harlequin or Ninja
Hunter/Ranger -> Trapper or Sniper
4th Class ~
Paladin/Myrmidon -> Dragoon or Destroyer
Oracle/Warmage -> Cleric or Archmage
Harlequin/Ninja -> Gambit or Shadow
Trapper/Sniper -> Sentinel or Howitzer
I know. Pretty complicated. For the "or" classes, you can choose whichever you want.