I discuss the construction of L-infinity algebras including
the special case of the Courant algebroid. Then I elaborate on the
general relation between the data of an L-infinity algebra and a
classical field theory in theoretical physics. It is argued that there is a
one-to-one correspondence between consistent field theories and
L-infinity algebras (up to reasonably defined isomorphisms),
with the gauge algebra, interactions, etc. of a field theory being
encoded in the higher brackets of an L-infinity algebra.
I discuss double field theory as a non-trivial example.