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This is a translation of an article appeared in Japanese in Suugaku 63(2011), no. 1, 43-66 (MR2790665) and is a survey of Lagrangian Floer homologywhich the author studies jointly with Y.-G.Oh, H. Ohta, and K. Ono. It alsocontains some explanation on its relation to (homological) mirror symmetry.

Floer homology of Lagrangian submanifolds