Cartan matrices and integrable lattice Toda field equations

Differential-difference integrable exponential-type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras A(2), B-2, C-2, G(2), the complete sets of integrals in both directions are found. For the simple Lie algebras of the classical series A(N), B-N, C-N and affine algebras of series D-N((2)), the corresponding systems are supplied with the Lax representation.