Based on the Shannon-Wiener approach to mathematical information theory, which allows for a mathematical measurement of the amount of information, the book begins with a distinction between the concepts of message and information, as well as the axiomatic assignment of an amount of information to a probability. The second part examines countable probability spaces, whose average amount of information leads to the definition of Shannon entropy. Three classical applications of Shannon entropy in statistical physics, mathematical statistics, and telecommunications are presented, along with an initial insight into the field of quantum information. The third part is dedicated to general probability spaces and specifically addresses the information-theoretic analysis of dynamic systems. The book builds on undergraduate knowledge and is primarily aimed at that audience.