Motivated by the recent discoveries of spin-1 and pseudo-spin-1 2 Bose gas, we have studied the general structure of the Bose gases with arbitrary spin. A general method is developed to uncover the elementary building blocks of the angular momentum eigenstates, as well as the relations (or interactions) between them. Applications of this method to Bose gas with integer spins (f=1,2,3) and half integer spins (f=1,2,3,2) reveal many surprising structures.