Geometric evolution equations have been used to study geometric questions like isoperimetric inequalities, the Poincar ́e conjecture, Thurston’s geometrization conjecture, the 1/4-pinching theo- rem, or Yau’s uniformization conjecture. In this course, I’ll give an introduction geometric evolution equations like Ricci flow, curve shortening flow, mean curvature flow and Gauss curvature flow. We will learn to compute evolution equations, study the singularities and the behavior of the evolution equations. At the end, I’ll indicate briefly, how evolution equations and surgery can be used to address geometric problems.