This volume is an exciting collection of short review articles written by leading international experts on the superconducting state in magnetic fields, a rapidly developing area. The philosophy of the book is to emphasize the importance of having experimental and theoretical works side by side. Every effort has been made to match each experimental article with a corresponding theoretical article. The selection of materials includes special topics, new effects and new trends concerning superconductors in low and high magnetic fields. The special topics and new trends include quantum and classical melting of the vortex lattice, new vortex lattice symmetries, vortex core states, nonlinear Meissner effect, symmetry of the order parameter in high-temperature superconductors, and superconductors in high magnetic fields. The book is targeted at a broad audience, including graduate students, postdocs and other researchers active or interested in this field.