This thesis attempts to contribute with some novel numerical methods in applied superconductivity, including a comprehensive discussion of the different mechanism involved in the vortex dynamics, as well as some relevant microscopic phenomena. The book has been structured in three parts. On the one hand, a general critical state theory for type-II superconductors with magnetic anisotropy, its computation, implications, and consequently some applications for particular problems, is what the first and second part try to convey. On the other hand, some microscopical aspects of the superconductivity have been also considered and the attained results have been compiled along the third part of this thesis.
