Many of the real-life applications (e.g., in banking/insurance, mechanics, medicine, etc.) can be only approached, modelled and computed as stochastic (or random) processes. The aim of this course is to introduce the most essential mathematical concepts and computational methods from the area of stochastic and random processes. Besides of gaining theoretical and practical backgrounds in the areas of stochastic calculus, random processes and uncertainty quantification, the participants will gain practical skills by doing supervised short research projects from real-life applications. The recurrent theme of the course is in establishing a joint stochastic/statistic perspective based on optimisation paradigm - for various computational methods and algorithms from computational science, machine learning and informatics.