This course is based on the concept of entropy, one of the most fundamental discoveries of human thought, and the application of Jaynes' "maximum entropy method" to determine the "most probable state" of a system composed of individual entities. Course participants will learn - in theory and application - the tremendous power of Jaynes' method for the analysis of engineering, scientific and human systems. To do this, it is first necessary to understand the concept of probability, and to appreciate the probabilistic basis of entropy. Topics include: Concept of probability, information theory, plausible reasoning, sampling theory. Orthodox and Bayesian statistical methods. Concept of entropy, Shannon entropy, cross-entropy, maximum entropy methods, Jaynes relations, fluctuation theory. Systems analysis: thermodynamics, Carnot efficiency, energy analysis, life cycle analysis, ecological indices. Other applications in fluid and solid mechanics, transport, logistics, commerce, social systems (topics will be selected based on students' interests). Non-Shannon entropies, inverse methods, transient processes.