Machine Learning: From the Classics to Deep Networks, Transformers and Diffusion Models, Third Edition starts with the basics, including least squares regression and maximum likelihood methods, Bayesian decision theory, logistic regression, and decision trees. It then progresses to more recent techniques, covering sparse modelling methods, learning in reproducing kernel Hilbert spaces and support vector machines. Bayesian learning is treated in detail with emphasis on the EM algorithm and its approximate variational versions with a focus on mixture modelling, regression and classification. Nonparametric Bayesian learning, including Gaussian, Chinese restaurant, and Indian buffet processes are also presented. Monte Carlo methods, particle filtering, probabilistic graphical models with emphasis on Bayesian networks and hidden Markov models are treated in detail. Dimensionality reduction and latent variables modelling are considered in depth. Neural networks and deep learning are thoroughly presented, starting from the perceptron rule and multilayer perceptrons and moving on to convolutional and recurrent neural networks, adversarial learning, capsule networks, deep belief networks, GANs, and VAEs. The book also covers the fundamentals on statistical parameter estimation and optimization algorithms. Focusing on the physical reasoning behind the mathematics, without sacrificing rigor, all methods and techniques are explained in depth, supported by examples and problems, providing an invaluable resource to the student and researcher for understanding and applying machine learning concepts.