This is the second volume in the annual series, Acta Numerica, a collection of invited survey papers encompassing all aspects of numerical analysis. Following the success of the first volume, this year's papers cover many of the core topics in numerical methods today. Papers on annealing problems, parallel methods, domain decomposition, and multigrid methods will enable anyone with an interest in computational and mathematical numerics to quickly grasp the latest developments and emerging trends in this diverse subject.