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We will describe an algebraic framework, which allows one to compute Lagrangian Floer homology HF(L0,L1) of two immersed curves on a surface. To a surface we assign a certain algebra. To each immersed curveÌýL we assign an A_infinity module M(L) (over the surface algebra). Then computing Lagrangian Floer homology reduces to aÌýcomputation of Hom(M(L0),M(L1)). We will describe this construction onÌýa particular example of a 2-sphere with four discs deleted.