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1 Introduction 1 I Fundamentals 3 2 Probability 5 3 Statistics 63 4 Graphical models 143 5 Information theory 217 6 Optimization 255 II Inference 337 7 Inference algorithms: an overview 339 8 Gaussian filtering and smoothing 353 9 Message passing algorithms 395 10 Variational inference 433 11 Monte Carlo methods 477 12 Markov chain Monte Carlo 493 13 Sequential Monte Carlo 537 III Prediction 567 14 Predictive models: an overview 569 15 Generalized linear models 583 16 Deep neural networks 623 17 Bayesian neural networks 639 18 Gaussian processes 673 19 Beyond the iid assumption 727 IV Generation 763 20 Generative models: an overview 765 21 Variational autoencoders 781 22 Autoregressive models 811 23 Normalizing flows 819 24 Energy-based models 839 25 Diffusion models 857 26 Generative adversarial networks 883 V Discovery 915 27 Discovery methods: an overview 917 28 Latent factor models 919 29 State-space models 969 30 Graph learning 1031 31 Nonparametric Bayesian models 1035 32 Representation learning 1037 33 Interpretability 1061 VI Action 1091 34 Decision making under uncertainty 1093 35 Reinforcement learning 1133 36 Causality 1171