This book addresses state of the art techniques which have rapidly evolved from the first studies of the Quantum Spin hall effect in graphene to more advanced algebraic topological invariants. Additionally, this book provides a comprehensive study of the topological properties of complex vector bundles endowed with actions of magnetic groups. Of particular interest is the description of the tools that will assist in performing the calculations of those invariants for prescribed spaces with magnetic symmetries. One relevant case is the determination of topological invariants in the electronic structure of magnetic crystals. The results of this book will aid researchers in finding the topological invariants of gapped Hamiltonians for specific magnetic symmetries in crystals.