  In this work we review various findings in the planar quantum physics with
the special emphasis on the two-component quantum electrodynamics in
three-dimensional spacetime (QED_{3}) with the Chern-Simons (CS) term. First
the classical electrodynamics is briefly outlined. Then we construct and
classify the unitary irreducible representations of the Poincare group and
connect them to various covariant fields. Subtleties with discrete symmetries
arising in QED_{3} are also discussed. Quantization of the free gauge field
with and without the CS term is performed in Coulomb gauge. Subsequently we
discuss the ultraviolet behavior of the theory in perturbative regime and
perform some one-loop calculations. The induced CS term is examined using the
effective action formalism. The non-relativistic electron-electron interactions
are considered in the Maxwell-Chern-Simons theory and the possibility of bound
states is briefly discussed. We also examine the non-relativistic scattering of
two anyons in the pure CS theory to one-loop order.
