Minimal surfaces are surfaces that locally minimize their area while having a fixed boundary. They are defined mathematically as surfaces with zero mean curvature, meaning that they curve equally in all directions. Common examples include soap films stretched across a wireframe and the Catenoid, which is a type of minimal surface formed by rotating a catenary curve. These surfaces are important in various fields, including mathematics, physics, and engineering. They can be studied using calculus of variations and have applications in materials science and architecture. The study of minimal surfaces also connects to the work of mathematicians like Bernhard Riemann and Joseph Plateau.