  We present an "algebraic treatment" of the analytical Bethe Ansatz. For this
purpose, we introduce abstract monodromy and transfer matrices which provide an
algebraic framework for the analytical Bethe Ansatz. It allows us to deal with
a generic gl(n)-spin chain possessing on each site an arbitrary
gl(n)-representation. For open spin chains, we use the classification of the
reflection matrices to treat all the diagonal boundary cases. As a result, we
obtain the Bethe equations in their full generality for closed and open spin
chains. The classifications of finite dimensional irreducible representations
for the Yangian (closed spin chains) and for the reflection algebras (open spin
chains) are directly linked to the calculation of the transfer matrix
eigenvalues. As examples, we recover the usual closed and open spin chains, we
treat the alternating spin chains and the closed spin chain with impurity.
