Global nonlinear dynamics in applied mechanics dates back to the Eighties, when the scientific community realized the importance of nonlinear phenomena in view of technical applications. Since then, the area has been evolving in a revolutionary way, with applications to a wide variety of systems made possible by sophisticated analytical, geometrical and computational techniques employing powerful concepts/tools of bifurcation and chaos theory, properly updated and complemented with a view to engineering aims and meaningful experimental verifications. The achievements occurred over the last thirty years entail a substantial change of perspective when dealing with vibration problems, and are deemed ready to meaningfully affect the analysis, control and design of mechanical/structural systems. This course aims at highlighting the important, yet still generally overlooked, role that the relevant concepts/tools may play as regards the load carrying capacity and safety of engineering systems. Attention is paid to the evolution and update of the old concept of stability, as ensuing from consideration of global dynamics. Upon dwelling on bifurcation and complexity, theoretical and practical stability, recent results obtained for a variety of systems in applied mechanics and structural dynamics are overviewed in terms of analysis and control of nonlinear phenomena. Local and global stability of systems are discussed by also considering the effects of imperfections or small, but finite, dynamical perturbations, along with variations of control parameters. All of them may arise in technical applications and experiments, and are to be properly considered in design in order to secure the system capability to sustain changes without modifying the desired outcome. Robustness of solutions against variations of initial conditions or control parameters, and system dynamical integrity, are fundamental concepts to be addressed in view of global phenomena, which may entail the existence of merely residual levels of robustness and integrity, unacceptable in technical applications. The overall transition from a local to global safety concept has also major implications as regards the feasibility and effectiveness of techniques aimed at controlling nonlinear dynamics, which may drastically change according to whether the control goal is local or overall. All these issues, which also permit to explain partial discrepancies between experimental and theoretical/ numerical results based on merely local analyses, are overviewed for systems from macro- to micro/nano- mechanics. Archetypal discrete systems and reduced order models of continuous systems are addressed. Specific phenomenological aspects are discussed, paying attention to the common or distinguishing nonlinear dynamical features expected to play a meaningful role in analysis and design engineering. The course is addressed to doctoral students and postdocs, but also to academics, industrial researchers and practicing engineers in mechanical, civil and aeronautical engineering, as well as in applied physics or applied mathematics.