This thesis has two parts, based on work carried out during my PhD. The first part comprises discussion of magneto-optical properties of ultra thin films of topological insulators (TI) with broken inversion symmetry. We explore the magneto-optical properties of thin film topological insulators (TFTI). Topological insulators are materials with insulating bulk and symmetry protected gapless surface states. In the TIs we consider, spin-Orbit Interaction (SOI) inverts valence and conduction bands and gapless surface states appear as the bulk gap closes at the interface of a topological insulator with conventional insulator. We study the magneto-optical response of ultrathin films of topological insulators in the presence of an external magnetic field with hybridization and broken inversion symmetry. We find that inversion symmetry breaking results in Landau level crossings and opening of additional optical transition channels. Inversion symmetry can be broken due to interaction with a substrate or electrical gating. A phase transition from normal to topological insulating phase occurs by tuning system parameters with measureable signatures in static (dc) and dynamic (optical) conductivity. Moreover, we find that the optical Hall conductivity plateaus remain robust against a significant range of disorder strength. In the second part we discuss Kondo effect in a complex Quantum Dot (QD) in the presence SOI and analyze its influence on fixed points and Kondo temperature. We model a quantum dot (QD) in the Coulomb blockade regime with two localized orbitals connected to two external leads with SOI in the leads. The lead electrons couple to the dot state in different angular momentum modes in the presence of SOI. We develop an effective Hamiltonian for the system and study the multiparameter RG flows by renormalization group analysis in the weak coupling regime. Previous studies have shown that in the absence of SOI for odd electrons in the dot SU(4) and SU(2) Kondo fixed points are stable and for even electrons a universal stable fixed point exists. We determine the fixed points in the presence of SOI. We determine the Kondo temperature by numerically solving the RG equations and show that the Kondo temperature is enhanced by the SOI.