This full-day course addresses the fundamental topic of stability in nonlinear microwave circuits and networks (MCNs), covering concepts, qualitative analysis, simulation, and engineering design. The many unique qualitative behaviors possible in common nonlinear MCNs will be illustrated, as well as the fundamental means by which these behaviors can abruptly arise with parameter changes (termed a bifurcation). Course attendees will learn about steady-state solutions, identify instability problems through small- and large-signal stability analysis, and understand dynamical mechanisms responsible for instabilities. The primary approaches for stability analysis (classical to advanced) will be presented and compared. Practical examples of instability, stability analysis, and stabilization design will be presented for MCNs such as power amplifiers, frequency multipliers/dividers, and voltage-controlled oscillators. Finally, the vast research area on harnessing nonlinear dynamics for engineering purposes will be surveyed, providing a glimpse into future nonlinear designs. The course will include video/hardware demonstrations and several live stability analysis sessions using ADS.