This book studies growth and decay processes, interacting populations and heating problems. The presented approach describes each problem from the beginning, i.e. starting from a real case, formulating a "word equation", building a suitable model (in general a differential equation), solving the equation both in a classical way and using computer software Maple or Matlab, and explaining results from various points of view. Necessary mathematical material and computer tools are included for the reader's convenience. The chapter list is: Introduction to mathematical modelling, Compartment models, Models of single populations, Numerical solution of differential equations, Interacting population models, Phase-plane analysis, Linearisation analysis, Some extended population models, Formulating basic heat models, Solving time dependent heat problems, Solving heat conduction problems, and Introduction to partial differential equations. The modelling approaches cover empirical, stochastic, simulation, deterministic and statistical models. Readers are expected to have some basic familiarity with differential equations. Supplementary material is in the appendices: Differential equations, Further mathematics, Notes on Maple and MATLAB, and Units and scaling. The book can be useful for students of mathematical modelling. They will find many skills for modelling and solving real problems. Useful sheets for Maple and MATLAB are included for numerical solution. The most important feature of the book is that it contains many real life examples. This shows at the same time how useful and close to real life mathematical methods are. The main examples are solved in detail and the others are left for the reader. This is the best treasury of real case problems seen in a single book.