In this chapter, an overview of the theory of probability, statistical and machine learning is made covering the main ideas and the most popular and widely used methods in this area. As a starting point, the randomness and determinism as well as the nature of the real-world problems are discussed. Then, the basic and well-known topics of the traditional probability theory and statistics including the probability mass and distribution, probability density and moments, density estimation, Bayesian and other branches of the probability theory, are recalled followed by a analysis. The well-known data pre-processing techniques, unsupervised and supervised machine learning methods are covered. These include a brief introduction of the distance metrics, normalization and standardization, feature selection, orthogonalization as well as a review of the most representative clustering, classification, regression and prediction approaches of various types. In the end, the topic of image processing is also briefly covered including the popular image transformation techniques, and a number of image feature extraction techniques at three different levels. © 2019, Springer Nature Switzerland AG.