Evolution algebras are not necessarily associative algebras.  must be satisfied, where  and  are two distinct basis elements. Moreover, structural constants of an evolution algebra are given by a quadratic matrix. In this paper, we describe the derivation of three-dimensional solvable and nilpotent evolution algebras and that of the two-dimensional subalgebra of complex evolution algebras.

solvable evolution algebras, nilpotent evolution algebras, subalgebras.