Delve into the second part of a comprehensive lecture on numerical relativity presented by Helvi Witek from the University of Illinois at IPAM's Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy Tutorial. Explore the theoretical foundations of numerical relativity, including the 3+1 decomposition of spacetime and Einstein's equations. Gain insights into the well-posedness of hyperbolic equations, well-posed formulations of Einstein's equations, and suitable coordinate choices for stable numerical simulations. Discover recommended textbooks for in-depth study and learn about the accompanying xTensor tutorial, which offers hands-on experience with a Mathematica notebook. Examine topics such as evolution equations, free evolution schemes, wave equations, harmonic gauge, and initial data for single black holes.