Introduces the geometry of submanifolds of space form and the application of new methods based on the holonomy of the normal connection. The monograph explores the central position of s- representations in the framework of submanifold geometry in space forms and presents three tools for their study-reduction of codimensions, Moore's lemma for local splitting, and the normal holonomy theorem-then applies the tool of normal holonomy to study isoparametric submanifolds and their focal manifolds, orbits of Lie group actions and homogeneous submanifolds, and homogeneous structures on submanifolds. Generalizations to submanifolds of Riemannian manifolds and symmetric spaces close out the book