This book focuses on the challenges of stability analysis and control synthesis for nonlinear dynamical systems, including stochastic systems, multi-agent systems, and nonholonomic systmes. With the adaptive Nussbaum design, this book investigates the asymptotic stabilization problem for nonlinear systems, addressing practical constraints such as physical limitations on system states to ensure safety. Furthermore, this book develops fixed-time stable design to enhance the dynamic performance, with strategies compensating for modeling inaccuracies and external disturbances. In addition, the adaptive Nussbaum design is extended to distributed bipartite consensus design for multi-agent systems and resilient feedback design for nonholonomic systems subject to false data injection. Given the 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.