With many concrete examples and questions this book provides an engaging accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. Developing all necessary prerequisite material from real analysis to functional analysis it gives nonspecialists the foundation to understand what evolution equations are and how to work with them in various areas of practice. The book covers 35 different models spanning chemical kinetics pharmacokinetics neural networks chemotaxis mathematical physics beam dynamics aeroelasticity infectious disease epidemiology combustion and environmental issues.