Abstract: Since the discovery of the integer quantum Hall effect by von Klitzing, Pepper and Dorda in 1980, there has been immense research to study topological properties in solid state systems, such as topological insulators, superconductors, semimetals and so on. In this seminar, I will talk about higher-order topological insulators and the invariants that classify their topology. Specifically, I will show the higher-order bulk-boundary correspondence in a family of generalized models with extended hopping terms and anti-commuting mirror symmetries. Using the symmetry structure of Wilson loops for this class of models, I will define a set of bulk Zinvariants that characterize their topology. Periodically driven (Floquet) systems also exhibit rich topological phases and some of these phases do not even have a static counterpart. In the second part of the seminar, I will talk about Floquet engineering of monolayer graphene using twisted light. Since twisted light breaks the space translational symmetry (as well as time reversal symmetry), I will discuss the real space topology of graphene and how by tuning the frequency of the external drive field we can generate multifold degeneracy.