This volume contains the proceedings of the First Workshop ``Matematicos Mexicanos Jovenes en el Mundo'', held from August 22-24, 2012, at Centro de Investigacion en Matematicas (CIMAT) in Guanajuato, Mexico. One of the main goals of this meeting was to present different research directions being pursued by young Mexican mathematicians based in other countries, such as Brazil, Canada, Colombia, Estonia, Germany, Spain and the United States, showcasing research lines currently underrepresented in Mexico. Featured are survey and research articles in six areas: algebra, analysis, applied...