A surface in the three-dimensional Euclidean space R ^ 3 is said to be minimal if its average curvature is equal to zero, this fact is of great importance in the physical principle of surface tension, its relation with the complex analysis and the characterizations that are can get; the works of Euler and Lagrange with differential equations allow us to find the first minimal surfaces and show their uniqueness, in addition Wieirstrass manages to determine the way in which we can construct minimal surfaces from holomorphic functions.