We studied the edge states and their roles in conductivity
and magnetism of graphene nanoribbions and flakes. we studied the Aharonov-Bohm effect in graphene nanodisks and rings. We described the quantum oscillations of the magnetization of graphene flakes. we have examined the snake-like states of transport
electrons in the configurations of graphene ribbons with a domain wall in the centre.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.