This book is devoted to the recent advances in the theory of local topological and geometric properties of mappings in n-dimensional Euclidean space. Quasiconformal, and quasiregular bi-Lipschitz mappings and the methods to study local behavior of this mappings without differentiability assumptions form the core of the book. In Part 1 the reader will find the necessary terminology, elementary facts and basic properties for such mappings. In Part 2 the fundamental concept of infinitesimal space quasiregular mapping at a point is introduced and its structure is described. The developed theory is applied in Part 3 to the study of local and boundary behavior of spatial mappings, their regularity, Hölder’s and Lipschitz’s continuity. It’s shown that the local injectivity of a mapping display in space is intimately connected to the BMO property of its dilatation tensor. This book is addressed to experts in modern geometric function theory as well as to, educators and the beginning researchers graduate students with a year’s background in real and complex variables seeking access to research topics.