This book takes readers on a multi-perspective tour through state-of-the-art mathematical
developments related to the numerical treatment of PDEs based on splines and in particular
isogeometric methods. A wide variety of research topics are covered ranging from approximation
theory to structured numerical linear algebra. More precisely the book provides (i) a
self-contained introduction to B-splines with special focus on approximation and hierarchical
refinement (ii) a broad survey of numerical schemes for control problems based on B-splines
and B-spline-type wavelets (iii) an exhaustive description of methods for computing and
analyzing the spectral distribution of discretization matrices and (iv) a detailed overview of
the mathematical and implementational aspects of isogeometric analysis. The text is the outcome
of a C.I.M.E. summer school held in Cetraro (Italy) July 2017 featuring four prominent
lecturers with different theoretical and application perspectives. The book may serve both as a
reference and an entry point into further research.
