IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs : Cetraro Italy 2012 Providing an introduction to isogeometric methods with a focus on their mathematical foundations this book is composed of four chapters each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations and gives an overview of geometric modeling techniques that can be used within the isogeometric approach with a focus on non tensor product splines. Finally it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations and treats in detail an application of fundamental importance: the isogeometric simulation of a viscous incompressible flow. Preface Standard and Non‐Standard CAGD Tool for Isogeometric Analysis: a Tutorial Models for Isogeometric Analysis from CAD An Introduction to the Numerical Analysis of Isogeometric Methods Isogeometric Compatible Discretizations for Viscous Incompressible Flow.