This book illustrates the latest progress on the hydrodynamic instabilities induced by a shock wave, particularly RM (Richtmyer-Meshkov) instability. The hydrodynamic instabilities play crucial roles in various industrial and scientific fields, such as inertial confinement fusion, supersonic combustion, supernova explosion, etc. This book experimentally and theoretically explores the shock-driven instabilities of complex gas-gas and gas-liquid interfaces. The main difficulty in performing an experimental study on RM instability, especially in a shock-tube circumstance, lies in creating an idealized initial interface because the RM instability is extremely sensitive to the initial condition. This book introduces new experimental methods to generate shape-controllable two-dimensional gaseous interfaces, thickness-controllable gas layers, and water droplets embedded with a vapour bubble in the shock-tube experiments. It covers the latest experiments and theories on the shock-driven hydrodynamic instabilities of multi-mode, multi-layer, and multi-phase interfaces. It explores the effects of the mode-competition, interface-coupling, and phase-transition on interface evolution, respectively. This book establishes a universal nonlinear theory to predict the RM instability of a shocked multi-mode interface based on spectrum analysis. This book quantifies the effects of interface-coupling and reverberating waves on the hydrodynamic instabilities of a shocked multi-layer interface. This book provides the experimental studies of the interaction of a shock wave and a multi-phase droplet and proposes a modified Rayleigh-Plesset equation to predict the vapour bubble collapse inside a droplet.