The book presents a case approach to mathematical modeling. It is written as a one-term course on modeling to be read by third year students of mathematics. The material covers several areas of mathematical applications in a very interesting way and pleasant style. Selected problems are studied, starting from the real situation before deriving the suitable mathematical model, solving and modifying it to obtain results that fit to the real situation. Chapters are devoted to the following problems: Crystallization Dynamics, Will the Valve hold?, How Much Will that Annuity Cost Me?, Dimensional analysis, Predator-Prey Systems, A Control Problem in Fishery Management, Formal Justice, Traffic Dynamics: A Microscopic Model, Traffic Dynamics: Macroscopic Modeling. Chapters end with examples and suggestions for further research. Some topics are “classical”, but several problems are rather new and cannot be found in other textbooks on modeling. This book can be used in seminars or for student mathematical modeling competitions.