  Recent advancements in the generation of mid-infrared and terahertz laser
pulses have enabled us to observe strong-field driven non-perturbative
high-harmonic generation (HHG) from semiconductors, dielectrics, and
semimetals. HHG has added another dimension to time-resolved ultrafast electron
dynamics in materials with unprecedented temporal resolution. Present thesis
discusses how HHG is an emerging method to probe static and dynamical
properties in two-dimensional materials. In this thesis, two-dimensional
materials with hexagonal symmetry are studied.
  We have demonstrated that the high-harmonic spectrum encodes the fingerprints
of electronic band structure and interband coupling between different bands.
Furthermore, by analysing gapped and gapless graphene, we show how electron
dynamics in a semimetal and a semiconductor are different as the harmonic
spectrum depends differently on the polarisation of the driving laser. To
explore the role of defects in HHG, spin-polarised vacancy defects in hexagonal
boron nitride are considered. It has been found that electron-electron
interaction is crucial for electron dynamics in a defected solid. In all cases,
we present how different symmetries of the lattice can be extracted from the
harmonic spectrum. Finally, a light-driven method is proposed for observing
valley-polarisation in pristine graphene, using a tailored laser pulse. Also, a
recipe is discussed to write and read valley-selective electron excitations in
materials with zero bandgap and zero Berry curvature.
