Model Formulation -- Spatial Components and Transport -- Parameterization -- Model Solution - Analytical Methods -- Model Solution -Numerical Methods -- Stability and Steady-State -- Multiple Time Scales and Equilibrium Processes -- Discrete Time Models -- Dynamic Programming -- Testing and Validating the Model -- Further Reading and References. Many texts on ecological models jump to describing either particular relations or computational results, without treating in detail the conceptual and mathematical basis of many steps in modelling: why set up models, what are basic conceptual models, how do conservation laws come in, how are models solved, what are steady states. This book is intended to bridge this gap. It is intended as an introductory text for graduate and post-graduate students, but also as a help for experienced ecologists who want to make more of their data by modelling. It contains many examples, all worked out in the open-source package R, providing the reader the opportunity to practice all methods and get hands-on experience. Audience: This book will be of interest to advanced undergraduate and graduate students in ecology, biology, geology, bio-engineering, and to some extent students from physics and chemistry.