This chapter will provide comprehensive insights into the captivating world of nonlinear dynamics. Initial section will introduce concept of state variables, phase space, different examples of continuous-time models, characteristics of fixed points. Key features of nonlinear systems, characteristics differ from linear systems are essential to observe inherent complexities in nonlinear dynamics. Next segment will describe features of discrete systems, stability and bifurcation scenario, occurrence of qualitative changes due to parameter variation. Then the chaos theory will be portrayed where sensitive dependence on initial conditions creates intriguing phenomenon. Accordingly chaos control and synchronization will be showcased. Further, the application of nonlinear systems in diverse fields will encourage the readers for a deep dive into the vast ocean of complex world. Those applications will emphasize the importance of computational techniques, numerical simulation via nonlinear tools.