Surveys -- An Introduction to Lattice Chiral Fermions -- Computing f(A)b for Matrix Functions f -- Computational Methods for the Fermion Determinant and the Link Between Overlap and Domain Wall Fermions -- Monte Carlo Simulations of Lattice QCD -- Lattice QCD -- Determinant and Order Statistics -- Monte Carlo Overrelaxation for SU(N) Gauge Theories -- Improved Staggered Fermions -- Perturbative Landau Gauge Mean Link Tadpole Improvement Factors -- Reversibility and Instabilities in Hybrid Monte Carlo Simulations -- A Finite Baryon Density Algorithm -- The Nucleon Mass in Chiral Effective Field Theory -- Computational Methods -- A Modular Iterative Solver Package in a Categorical Language -- Iterative Linear System Solvers with Approximate Matrix-vector Products -- What Can Lattice QCD Theorists Learn from NMR Spectroscopists? -- Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov SubspaceMethods -- Fast Evaluation of Zolotarev Coefficients -- The Overlap Dirac Operator as a Continued Fraction.