Book excerpt: This volume contains papers by the main participants in the meeting of the 6th International Colloquium on Differential Geometry and its Related Fields (ICDG2018). The volume consists of papers devoted to the study of recent topics in geometric structures on manifolds -- which are related to complex analysis, symmetric spaces and surface theory -- and also in discrete mathematics. Thus, it presents a broad overview of differential geometry and provides up-to-date information to researchers and young scientists in this field, and also to those working in the wide spectrum of mathematics.