Minimal surfaces are ubiquitous in nature. From butterfly wings to sea urchin plates, minimal surfaces serve to create structures with enhanced properties, including stiffness, thereby attracting the attention from material scientists and biologists. This chapter provides an in-depth introduction to minimal surfaces by first examining their counterpart in experimental applications, zero equipotential surfaces, which are more familiar to people as a lead-in. A comprehensive mathematical background of differential geometry necessary for understanding minimal surfaces and a thorough the derivation of minimal surfaces, including the Weierstrass representation, is developed from a mathematical viewpoint.