Abstract: As the world gets increasingly connected, nonlocal interactions and nonlocal modeling start to

receive more attention. This lecture presents an introduction to nonlocal models, their mathematics,

computation, and application. We sample our recent attempts in the development of a systematic

mathematical framework for nonlocal models. Various applications are considered including mechanics,

diffusion and deep learning. We also draw connections with traditional local continuum models, discrete and fractional models and other relevant mathematical subjects.