  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 homology
which the author studies jointly with Y.-G.Oh, H. Ohta, and K. Ono. It also
contains some explanation on its relation to (homological) mirror symmetry.
