This book focuses on the challenges of stability analysis and control synthesis for complex nonlinear dynamical systems, including stochastic systems, multi-agent systems, and nonholonomic motion planning.  With Nussbaum design,  it introduces readers to the asymptotic stability problem for nonlinear systems, addressing practical constraints such as physical limitations on system states to ensure robustness. Furthermore, It presents readers with fixed-time stability for enhancing dynamic performance, with strategies that compensate for modeling inaccuracies and external disturbances. Then, the results are extended to multi-agent coordination, including consensus and bipartite consensus, and advanced feedback designs for nonholonomic systems to overcome motion constraints and ensure stability. Given its scope, the book offers an essential reference guide for researchers and engineers working on advanced nonlinear system control, as well as a valuable resource for upper-level undergraduate and graduate students.