This book is a collective work made by various authors well-recognised owing to their appreciable contributions to the theory and applications of probability. Both mathematical and engineering aspects of probability outline its framework. Readers can find here several timely topics such as risk theory and applications, Laplace distributions which describe the heavy-tailed noise, Poisson sums having applications in business and engineering, Markov chains investigations and approximations, Berstein-Hoeffding-type exponential inequalities useful for proving limiting theorems, Bayesian computational methods, as well as a modern view on sampling and reconstruction of Gaussian and non-Gaussian random processes.