  These lecture notes yield an introduction to quantum Hall effects both for
non-relativistic electrons in conventional 2D electron gases (such as in
semiconductor heterostructures) and relativistic electrons in graphene. After a
brief historical overview in chapter 1, we discuss in detail the kinetic-energy
quantisation of non-relativistic and the relativistic electrons in a strong
magnetic field (chapter 2). Chapter 3 is devoted to the transport
characteristics of the integer quantum Hall effect, and the basic aspects of
the fractional quantum Hall effect are described in chapter 4. In chapter 5, we
briefly discuss several multicomponent quantum Hall systems, namely the quantum
Hall ferromagnetism, bilayer systems and graphene that may be viewed as a
four-component system.
