Minimal surfaces are central objects in differential geometry. They are surfaces that locally minimize area, meaning that they have the smallest possible surface area for a given boundary. These objects have been used extensively to model physical phenomena, such as soap films and black holes. In the last decade, there has been renewed interest in minimal surfaces, leading to new techniques and directions in this field. This has led to a flourishing of research on the relationships between the structure of the set of minimal surfaces in a space and the shape of the set of surfaces that can be considered in it. The significance of the theory and the objects it involves is shown through beautiful applications on the abundance of minimal surfaces and close relations with the spectral problem. The aim of this project is to explore methods for controlling and classifying the minimal surfaces and related quantities that arise naturally when dealing with spaces that are relevant in differential geometry and general relativity.