In Algebraic Geometry, a singular point of a variety is one where the tangent space fails to be defined, therefore stopping the variety from being smooth (which is always the best situation). Fortunately, in certain cases, there are ways to make these singularities 'disappear', while keeping some properties of the original structure. I will talk about the method of blowing-up through some examples. This talk will be entirely self contained. In particular, there will be absolutely no mention of either sheaves or schemes, or any previous encounters with algebraic geometry.