2016 Nobel prize in physics: D. Thouless and topology of quantum transport

The 2016 Physics  Nobel prize was awarded to Thouless and Kosterlitz for the discovery of a new kind of phase transition and to Thouless and Haldane for the discovery of the topological meaning of the Quantum Hall conductance. 

I shall describe Thouless original finding that the Hall conductance is related to a topological invariant known as Chern number. No  background in topology or condensed matter physics will be assumed.