This monograph presents the complete theory of smooth quasigroups and loops, as well as its geometric and algebraic applications. Based on a generalisation of the Lie-group theory, it establishes new backgrounds for differential geometry in the form of nonlinear geometric algebra and `loopuscular' geometry. It will prove useful in applications in such diverse fields as mathematical physics, relativity, Poisson and symplectic mechanics, quantum gravity, dislocation theory, etc.
Audience: This volume will be of interest to researchers, lecturers and postgraduate students whose work involves geometry, group theory, nonassociative rings and algebras, and mathematical and theoretical physics.