A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

1.The Riemannian and Lorentzian Splitting Theorems.- 2.Periodic trajectories of dynamical systems having a one-parameter group of symmetries.- 3.Geometry and Materials.- 4.On deciding whether a submanifold is parabolic or hyperbolic using its mean curvature.- 5.Contact Forms in Geometry and Topology.- 6.Farkas and Janos Bolyai.- 7.Spectrum Estimates and Applications to Geometry.- 8.Variational problems on curves.- 9.Special Submanifolds in Hermitian Manifolds.- 10.An introduction to certain topics on Lorentzian geometry.