  We develop a new approach to Lagrangian-Floer gluing. The construction of the
gluing map is based on the intersection theory in some Hilbert manifold of
paths $\mathcal{P} $. We consider some moduli spaces of perturbed holomorphic
curves whose domains are either strips or more general Riemann surfaces with
strip-like ends. These moduli spaces can be injectively immersed into the
Hilbert manifold $\mathcal{P} $ by taking the restriction to non-Lagrangian
boundary.
  Some subsets $ \mathcal{M}^T(U) $ and $ \mathcal{M}^{\infty} (U) $ of the
aforementioned moduli spaces of perturbed holomorphic strips turn out to be
embedded submanifolds of the Hilbert manifold $ \mathcal{P} $. The main result
is that $ \mathcal{M}^T (U) $ converges in the $C^1 $ topology toward $
\mathcal{M}^{\infty} (U) $. As an application of this convergence property we
prove various gluing theorems.
  We explain the construction of Lagrangian-Floer homology and prove that the
square of the boundary map is equal to zero in the monotone case with minimal
Maslov number at least three. We also prove the invariance of the homology and
include the exposition of the Lagrangian-Floer-Donaldson functor and Seidel
homomorphism.
