Introduction.- Linear Perturbations in Galileon Gravity Models.- The Observational Status of Galileon Gravity After Planck.- Spherical Collapse in Galileon Gravity .- N-body Simulations and Halo Modelling in Galileon Gravity Cosmologies.- Nonlinear Structure Formation in Nonlocal Gravity.- Lensing by Clusters and Voids in Modified Lensing Potentials.- Summary, Conclusions and Future Work.
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