The Mathematics Education of Prospective Secondary Teachers Around the World Main Topics You Can Find in this “ICME 13 Topical Survey” Introduction Survey on the State of the art Summary and Looking Ahead.’ Update the TOC after the manuscript has been received This volume shares and discusses significant new trends and developments in research and practices related to various aspects of preparing prospective secondary mathematics teachers from 2005 2015. It provides both an overview of the current state of the art and outstanding recent research reports from an international perspective. The authors completed a thorough review of the literature by examining major journals in the field of mathematics education and other journals related to teacher education and technology. The systematic review includes four major themes: field experiences; technologies tools and resources; teachers knowledge; and teachers professional identities. Each of them is presented regarding theoretical perspectives methodologies and major findings. Then the authors discuss what is known in the field and what we still need to know related to the major topics