Dimension reduction is defined as the process of mapping high-dimensional data to a lowerdimensional vector space. Most machine learning and data mining techniques may not be effective for high-dimensional data. In order to handle this data adequately, its dimensionality needs to be reduced. Dimensionality reduction is also needed for visualization, graph embedding, image retrieval and a variety of applications. This paper discuss the most popular linear dimensionality reduction method Principal Component Analysis and the various non linear dimensionality reduction methods such as Multidimensional scaling, Isomap, Locally Linear Embedding, Laplacian Eigen Map, Semidefinite embedding, Minimum Volume Embedding and Structure Preserving Embedding .