  We use the dictionary between general field theories and strongly homotopy
algebras to provide an algebraic formulation of the procedure of integrating
out of degrees of freedom in terms of homotopy transfer. This includes more
general effective theories in which some massive modes are kept while other
modes of a comparable mass scale are integrated out, as first explored by Sen
in the context of closed string field theory. We treat $L_\infty$-algebras both
in terms of a nilpotent coderivation and, on the dual space, in terms of a
nilpotent derivation (corresponding to the BRST charge of the field theory) and
provide explicit formulas for homotopy transfer. These are then shown to govern
the integrating out of degrees of freedom at tree level, while the
generalization to loop level will be explored in a sequel to this paper.
