�@In this talk, I will explain some recent improvement 
of the Floer theory of Lagrangian submanifolds 
emphasising its application to Mirror symmetry. <BR>
The fundamental chain of the moduli space of the 
pseudoholomorphic disks gives a solution of Maurer 
Cartan equation on Loop space homology. 
It gives a Floer theory which has cyclic symmetry and 
converges in appropriate non Archimedian sense. 
The construction of virtual fundamental chain requires new 
technique based on continuous family of perturbation and 
on De Rham theory.  Using this technique we can keep more 
symmetry to obtain virtual fundamental chains.