Inspired by the recent algebraic approach to classical field theory, we
propose a more general setting based on the manifold of smooth sections of a
non-trivial fiber bundle. Central is the notion of observables over such
sections, i.e. appropriate smooth functions on them. The kinematic will be
further specified by means of the Peierls brackets, which in turn are defined
via the causal propagators of linearized field equations. We shall compare the
formalism we use with the more traditional ones.