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This is an expository article on the theory of Kuranishi structure and isbased on a series of pdf files we uploaded for the discussion of the googlegroup named `Kuranishi' (with its administrator H. Hofer). There we replied toseveral questions concerning Kuranishi structure raised by K. Wehrheim. At thisstage we submit this article to the e-print arXiv, all the questions orobjections asked in that google group were answered, supplemented or confutedby us. We first discuss the abstract theory of Kuranishi structure and virtualfundamental chain/cycle. This part can be read independently from other parts.We then describe the construction of Kuranishi structure on the moduli space ofpseudoholomorphic curves, including the complete analytic detail of the gluingconstruction as well as the smoothness of the resulting Kuranishi structure.The case of S^1 equivariant Kuranishi structure which appears in the study oftime independent Hamiltonian and the moduli space of Floer's equation isincluded.

Technical details on Kuranishi structure and virtual fundamental chain