  In this article we address two issues. First, we explore to what extent the
techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to
Lagrangian Floer homology. In [PSS96] an isomorphism between Hamiltonian Floer
homology and the singular homology is established. In contrast, Lagrangian
Floer homology is not isomorphic to the singular homology of the Lagrangian
submanifold, in general. Depending on the minimal Maslov number, we construct
for certain degrees two homomorphisms between Lagrangian Floer homology and
singular homology. In degrees where both maps are defined we prove them to be
isomorphisms. Examples show that this statement is sharp.
  Second, we construct two comparison homomorphisms between Lagrangian and
Hamiltonian Floer homology. They underly no degree restrictions and are proven
to be the natural analogs to the homomorphisms in singular homology induced by
the inclusion map of the Lagrangian submanifold into the ambient symplectic
manifold.
