Ecological resilience describes systems that have the capacity to recover after a complete collapse of system function. For a system to be ecologically resilient, system collapse is accepted as being inevitable and requires that the resources for subsequent system recovery be buried in the wreckage of that collapse. The ecological concept of a regime shift plays an important role in enhancing the ecological resilience of a dynamical system. Managing regime shifts that trigger system collapse provides a way to conserve existing system function. Managing regime shifts that systematically rebuild lost system function provides a way to restore lost system function. In this monograph, the author formalizes the ecologist's regime shift concept that allows the identification of two distinct regime shift mechanisms, shock-induced and bifurcation-induced regime shift, before defining ecological resilience as a regime transition system. The author takes the reader through the theoretical concepts in a tutorial nature and goes on to demonstrate practical applications of the theory. Written in a clear and accessible manner, this monograph is an illuminating introduction to a topic that has increasing importance in modern systems. This is important reading for both researchers and practitioners.