Preface; 1. Oscillations over long times in numerical Hamiltonian systems E. Hairer and C. Lubich; 2. Highly oscillatory quadrature D. Huybrechs and S. Olver; 3. Rapid function approximation by modified Fourier series D. Huybrechs and S. Olver; 4. Approximation of high frequency wave propagation M. Motamed and O. Runborg; 5. Wavelet-based numerical homogenization B. Engquist and O. Runborg; 6. Plane wave methods for approximating the time harmonic wave equation T. Luostari, T. Huttunen and P. Monk; 7. Boundary integral methods in high frequency scattering S. N. Chandler-Wilde and I. G. Graham; 8. Novel analytical and numerical methods for elliptic boundary value problems A. S. Fokas and E. A. Spence.