This book summarizes some of the most exciting developments that took place over the last decade regarding topological phenomena in spin-orbit-coupled condensed matter systems. Key topics discussed are the topological origin of anomalous Hall effects in solids, its extension to incorporate spin Hall effects and its quantization, topological phenomena originating from spin texture, topological insulators, and other forms of exotic topological matter. The topics are presented at a pedagogical level accessible to graduate students who finished a course in traditional solid state physics. Concepts originally invented in the context of particle physics, now heavily used in topological condensed matter, are presented at a level easily accessible to scientists without prior training in that discipline. The book provides an introduction and a survey of what underlies the modern theory of topological phenomena driven by spin-orbit coupling.