Summary: The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.