In this lecture I will give a brief overview on the theoretical foundations of numerical relativity. I will describe the 3+1 decomposition of spacetime and of Einstein’s equations. I will touch upon well-posedness of hyberbolic equations, mention well-posed formulations of Einstein’s equations and present suitable coordinate choices for stable numerical simulations. The presentation should be taken as a brief overview and what-is-what of the topic. To study Numerical Relativity in depth, I recommend the excellent textbooks by M. Alcubierre 2008, Baumgarte & Shapiro 2010, Shibata 2015 and Baumgarte & Shapiro 2021. "The xTensor tutorial on Monday, 20 September 2021, is a hands-on tutorial. To run the mathematica notebook live, please download it from the box folder: https://uofi.box.com/s/cokg7uw4bds07fj44yo6mt16urml578o You will also need to install the *free* mathematica package xAct / xTensor from their website xAct.es"