This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry. This book contains a collection of articles of highest scientific standard. It provides an excellent introduction and overview of recent topics from multivariate approximation. It is a valuable source of references for specialists in the field. It is a representation of the state-of-the-art in selected areas of multivariate approximation. It gives a rigorous mathematical introduction to special topics of interdisciplinary research.