Dimensionality reduction is to map high-dimensional data into low-dimensional representation while retaining the intrinsic properties in data. This chapter first elaborates on the problem and definition, the working principle employing formal and illustrated descriptions, and the related elements of dimensionality reduction. Next, we discuss linear dimensionality reduction, nonlinear dimensionality reduction, and deep dimensionality reduction separately, in which the linear dimensionality reduction can be divided to linear subspace learning and multilinear subspace learning. Nonlinear dimensionality reduction includes distance matrix method, kernel method, manifold learning, and neighborhood embedding. Moreover, deep dimensionality reduction is mainly based on deep autoencoders and variational autoencoders. We also expound several typical algorithms for dimensionality reduction, such as principal component analysis (PCA), multidimensional scaling (MDS), isometric feature mapping (Isomap), local linear embeddings (LLE), stochastic neighbor embedding (SNE), and t-distributed stochastic neighbor embedding (t-SNE). Finally, the application fields of dimensionality reduction are briefly introduced.