Featuring the clearly presented and expertly-refereed contributions of leading researchers in the field of approximation theory, this volume is a collection of the best contributions at the Third International Conference on Applied Mathematics and Approximation Theory, an international conference held at TOBB University of Economics and Technology in Ankara, Turkey, on May 28-31, 2015. The goal of the conference, and this volume, is to bring together key work from researchers in all areas of approximation theory, covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. These topics are presented both within their traditional context of approximation theory, while also focusing on their connections to applied mathematics. As a result, this collection will be an invaluable resource for researchers in applied mathematics, engineering and statistics.