The book differs from most texts on dynamical system by blending the use of computer simulations with inquiry-based learning (IBL). Inquiry-based learning is an excellent tool to move students from merely remembering the material, to deeper understanding and analysis. The method relies on asking students questions first, rather than presenting the material in a lecture. Another unique feature is the use of computer simulations. Students can discover examples and counterexamples through manipulations built into the software. These tools have long been used in the study of dynamical systems to visualize chaotic behavior. We refer to this unique approach to teaching mathematics as ECAP for Explore, Conjecture, Apply, and Prove. ECAP was developed to mimic the actual practice of mathematics in an effort to provide students with a more holistic mathematical experience. In general, each section begins with exercises guiding students through explorations of the featured concept and concludes with exercises that help the student formally prove the result. While symbolic dynamics is a standard topic in an undergraduate dynamics text, we have tried to emphasize it in a way that is more detailed and inclusive than is typically the case. Finally, we have chosen to include multiple sections on important ideas from analysis and topology independent from their application to dynamics.