  This document is a reorganization of the results on the Master Thesis of the
same title written by the author under the supervision of Dr. Christian
Blohmann at the University of Bonn in 2014.
  There are three main results in this document.
  The first one is a construction of a high L-infinity algebra out of any
Gerstenhaber algebra. The second one uses a cochain null-homotopy from the
Chevalley-Eilenberg complex associated to a graded Lie algebra to any cochain
complex D to induce (transfer) the L-infinity algebra structure from the Lie
alegebra to Q(D), a resolution of D. Lastly, the third one establishes the
equivalence between cochain-homotopies to Q(D) and L-infinity algebra lifts
satisfying certain properties.
  All the three results are motivated from the study of multi-symplectic
structures. In particular, the definition of comomentum maps in
multi-symplectic manifolds.
