The purpose of this Open Access compendium, written by experienced researchers in mathematics education, is to serve as a resource for early career researchers in furthering their knowledge of the state of the field and disseminating their research through publishing. To accomplish this, the book is split into four sections: Empirical Methods, Important Mathematics Education Themes, Academic Writing and Academic Publishing, and a section Looking Ahead. The chapters are based on workshops that were presented in the Early Career Researcher Day at the 13th International Congress on Mathematical Education (ICME-13). The combination of presentations on methodological approaches and theoretical perspectives shaping the field in mathematics education research, as well as the strong emphasis on academic writing and publishing, offered strong insight into the theoretical and empirical bases of research in mathematics education for early career researchers in this field. Based on these presentations, the book provides a state-of-the-art overview of important theories from mathematics education and the broad variety of empirical approaches currently widely used in mathematics education research. This compendium supports early career researchers in selecting adequate theoretical approaches and adopting the most appropriate methodological approaches for their own research. Furthermore, it helps early career researchers in mathematics education to avoid common pitfalls and problems while writing up their research and it provides them with an overview of the most important journals for research in mathematics education, helping them to select the right venue for publishing and disseminating their work. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.