This book employs a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. A survey that can be taught in a single academic term is provided, and it covers a greater variety of dynamical systems (discrete vs continuous time, finite vs infinite-dimensional, dissipative vs conservative) than are normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics, such as solution maps and invariant manifolds, are presented.