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I will present a joint work with Martin Li. Minimal surfaces withÌýfreeÌýboundaryÌýare natural critical points of the area functional in compact smooth manifolds withÌýboundary. In this talk, I will describe a general existence theory for minimal surfaces withÌýfreeÌýboundary. In particular, I will show the existence of a smooth embedded minimal hypersurface withÌýfreeÌýboundaryÌýin any compact smooth Euclidean domain. The minimal surfaces withÌýfreeÌýboundaryÌýwere constructed using theÌýmin-maxÌýmethod. Our result allows the min-max free boundary minimal hypersurface to be improper; nonetheless the hypersurface is still regular.