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This dissertation is devoted to Coifman-Meyer multilinear operators and multiple weighted norm，inequalities in harmonic analysis. First, we will not only review the origin of multilinear operators, but also represent the twobranches of the theory.Then leading results on Coifman-Meyer multilinear singular integral willbe listed.Next we will give an introduction to the theory of multiple weights.Maximal operatorof singular integral will also be mentioned. An improved multiple Cotlars inequality will beobtained.By this result, weighted norm inequality for maximal operator of multilinear singularintegral including weak and strong estimates will be renewed under the multiple weights. Second, a class of multiple fractional type weights will be constructed.And we will get thenecessary condition for the characterization of that weights.Both strong and weak weightednorm inequalities for some multilinear fractional type operators (e.g.fractional maximal op-erator, fractional integral, commutators of fractional integral operators) will be obtained.Asapplications of these results, we will give some weighted estimates for the above operators withrough homogeneous kernels when suitable conditions were assumed on the kernels. Weightedstrong and some endpoint estimates for commutators of multilinear fractional integral operatorswill also be established. Third, the classical Marcinkiewicz integral will be generalized in the multilinear settings.We will apply the method for singular integral to prove an endpoint estimates for multilinearMarcinkiewicz integral.The weighted results for C will be obtained ir virtue.of a sharp estimate.Additionally, we will define a inultilinear version of area integral of , Lusin .and obtainedendpoint estimate for it. Finally, we will summarize tools in common use and unsolved problems with some details inthe appendix.