This course will present a subset of the mathematical techniques often use to gain an understanding of the response of complex systems to acute events and compound threats. Examples of complex systems include: installations, organizations, communities, etc. With the understanding of resilience as ability to withstand and 'bounce back' from major disruptive events, the course will consider resilience as an emergent attribute, and investigate some pre- and post-event approaches to resilience enhancement. The focus of the mathematical modeling techniques presented in this course will be on nonlinear dynamics. We will also discuss relevant variational optimization techniques that can be used to guide measures taken to enhance resilience. The course will include selected applications as case studies; examples include: savanna ecosystems, large installations, communities facing infectious diseases, preparation for and response to coastal storms, etc.