A new algorithm(LTSA) was proposed in this article for nonlinear manifold learning and nonlinear dimension reduction. The author used construction of local tangent spaces to represent local geometry and the global alignment of the local tangent spaces to obtain the the global coordinate system for the underlying manifold. Then it provided some error analysis to exhibit the interplay of approximation accuracy, sampling density, noise level and curvature structure of the manifold. At the same time, it compared LTSA with local linear embedding(LLE), which showed using LTSA can potentially detect the intrinsic dimension of the underlying manifold by analyzing the local tangent space structure. Last it listed several issues which deserved further investigation.