Chapter 1: Introduction -- Part 1: Preliminaries and Background -- Chapter 2: Background on Linear Algebra -- Chapter 3: Background on Kernels -- Chapter 4: Background on Optimization -- Part 2: Spectral dimensionality Reduction -- Chapter 5: Principal Component Analysis -- Chapter 6: Fisher Discriminant Analysis -- Chapter 7: Multidimensional Scaling, Sammon Mapping, and Isomap -- Chapter 8: Locally Linear Embedding -- Chapter 9: Laplacian-based Dimensionality Reduction -- Chapter 10: Unified Spectral Framework and Maximum Variance Unfolding -- Chapter 11: Spectral Metric Learning -- Part 3: Probabilistic Dimensionality Reduction -- Chapter 12: Factor Analysis and Probabilistic Principal Component Analysis -- Chapter 13: Probabilistic Metric Learning -- Chapter 14: Random Projection -- Chapter 15: Sufficient Dimension Reduction and Kernel Dimension Reduction -- Chapter 16: Stochastic Neighbour Embedding -- Chapter 17: Uniform Manifold Approximation and Projection (UMAP) -- Part 4: Neural Network-based Dimensionality Reduction -- Chapter 18: Restricted Boltzmann Machine and Deep Belief Network -- Chapter 19: Deep Metric Learning -- Chapter 20: Variational Autoencoders -- Chapter 21: Adversarial Autoencoders.