  The Flory theory for a single polymer chain is derived as the lowest order of
a cumulant expansion. In this approach, the full original Flory free energy
(including the logarithmic term), is recovered. %This term does not change the
wandering exponent $ \nu $ but turns out to %be responsible for the crossover
from Brownian $ (d>4) $ to swollen $ %(d\leq4) $ %regime. The prefactors of the
elastic and repulsive energy are calculated from the microscopic parameters.
The method can be applied to other types of monomer-monomer interactions, and
the case of a single chain in a bad solvent is discussed . The method is easily
generalized to many chain systems (polymers in solutions), yielding the usual
crossovers with chain concentration. Finally, this method is suitable for a
systematic expansion around the Flory theory. The corrections to Flory theory
consist of extensive terms (proportional to the number $N$ of monomers) and
powers of $N^{2-\nu d}$ . These last terms diverge in the thermodynamic limit,
but less rapidly than the usual Fixman expansion in $N^{2- d/2}$.
