Orbifolds are among the simplest generalizations of manifolds that include singularities. The main examples are quotients of a manifold under a proper discontinuous action of a group with finite isotropy groups. For instance, the classical plane tessellations can be neatly described using 2-dimensional orbifolds. Orbifolds appear naturally in many areas of mathematics. 

Hosted by the Spanish Topology Network, this course is tailored for general mathematicians at a graduate level and will cover the basics and some of the main developments of the theme. The lecturers, experts of recognized prestige in this field, will exhibit a selection of  the most relevant results concerning orbifolds and of the appearances of these objects in different mathematical areas. 

This course offers a valuable opportunity to understand the fundamentals and nuances  of these important mathematical objects.