This interactive Mathematica notebook provides a ready-made tool by which users can undertake their own mathematical experiments and explore the behavior of nonlinear systems, from chaos in low-dimensional maps and coupled ordinary differential equations to solitons and coherent structures in nonlinear partial differential equations and 'intrinsic localized modes' and 'discrete breathers' in extended lattice systems. The Mathematica format produces detailed numerical solutions and high quality graphics to help users develop a deeper understanding of nonlinear systems by exploring their behavior in real time. It also allows users to modify the existing templates to study other systems of their own choice. This software can supplement nonlinear dynamics courses and is also ideal for graduate students and researchers working in this field. Suitable for Windows XP, Windows Vista, Windows 7, Mac OS X and Linux. This software will run with Mathematica versions 5.2, 6.0, 7.0 and 8.0.