  In this review we present some of the work done in India in the area of
driven and out-of-equilibrium systems with topological phases. After presenting
some well-known examples of topological systems in one and two dimensions, we
discuss the effects of periodic driving in some of them. We discuss the unitary
as well as the non-unitary dynamical preparation of topologically non-trivial
states in one and two dimensional systems. We then discuss the effects of
Majorana end modes on transport through a Kitaev chain and a junction of three
Kitaev chains. Transport through the surface states of a three-dimensional
topological insulator is discussed. The effects of hybridization between the
top and bottom surfaces and the application of electromagnetic radiation on a
strip-like region on the top surface are described. Two unusual topological
systems are mentioned briefly, namely, a spin system on a kagome lattice and a
Josephson junction of three superconducting wires. We have also included a
pedagogical discussion on topology and topological invariants in the
appendices, where the connection between topological properties and the
intrinsic geometry of quantum states is also elucidated.
