This article investigates the relationship between various classes of nonassociative structures and generalized symmetric spaces. The classical example for this strategy is the definition of symmetric spaces as manifolds with multiplication as described by O. Loos. The authors review various classes of \(M\)-loops, satisfying additional properties. They start with a detailed review of the basic concepts, describing relations between algebraic and geometric structures. Later some parts of an infinitesimal theory of \(M\)-loops are developed.
For the entire collection see [Zbl 1194.00070].