  This is a research monograph on symplectic cohomology (disguised as an
advanced graduate textbook), which provides a construction of this version of
Hamiltonian Floer cohomology for cotangent bundles of closed manifolds. The
focus is on the aspects of the theory that have been neglected in the
literature: (1) the base is not assumed to be orientable or Spin, (2) local
systems on the free loop space are used to define twisted versions of Floer
cohomology, (3) a (twisted) Batalin-Vilkovisky structure is constructed, and
(4) the BV relation is verified. In this setting (i.e. with all the appropriate
twists), a proof of Viterbo's theorem relating symplectic cohomology to the
homology of the free loop space is provided, and we show that this map respects
the BV structure. Viterbo's theorem is proved by constructing three different
maps relating the two sides, and proving that two of the compositions are
isomorphisms by using degenerations of moduli spaces of genus 0 Riemann
surfaces with boundary. Two of the maps constructed are new, and use ideas
inspired by a Lagrangian version of family Floer cohomology.
