  Toda field theories are important integrable systems. They can be regarded as
constrained WZNW models, and this viewpoint helps to give their explicit
general solutions, especially when a Drinfeld-Sokolov gauge is used. The main
objective of this paper is to carry out this approach of solving the Toda field
theories for the classical Lie algebras. In this process, we discover and prove
some algebraic identities for principal minors of special matrices. The known
elegant solutions of Leznov fit in our scheme in the sense that they are the
general solutions to our conditions discovered in this solving process. To
prove this, we find and prove some differential identities for iterated
integrals. It can be said that altogether our paper gives complete mathematical
proofs for Leznov's solutions.
