Everyone knows what a two dimensional surface is. If we allow surfaces to bend or stretch, but not rip and tear, how many fundamentally different surfaces are there? The answer is known since the 1860's but it hasn't lost its simple elegance since: Everything can be obtained by cutting a number of holes into a sphere and glueing into some of them either handles or Möbius strips. We present the simple ZIP proof due to Conway and we will draw lots and lots of pictures. No formulas needed!