This book is an introduction to the mathematical description of information in science and engineering. The necessary ma- thematical theory will be treated in a more vivid way than in the usual theoretical proof structure. This enables the reader to develop an idea of the connections between diffe- rent information measures and to understand the trains of thoughts in their derivation. As there exist a great number of different possible ways to describe information, these measures are presented in a coherent manner. Some examples of the information measures examined are: Shannon informati- on, applied in coding theory; Akaike information criterion, used in system identification to determine auto-regressive models and in neural networks to identify the number of neu- rons; and Cramer-Rao bound or Fisher information, describing the minimal variances achieved by unbiased estimators.