This Master’s thesis investigates the effects of single and dual impurity potentials on the electronic properties of both pristine and gapped graphene, being examples of two-dimensional materials. The behavior of 2D materials at the atomic levels, particularly graphene, has been of interest due to their particular electronic properties, such as high electron mobility at certain conditions. The presence of impurities may significantly influence these properties, providing a modifiable platform for rearranging electronic characteristics for diverse applications. Our research focuses on how the impurity states that emerge, especially around energies at low DOS, affect the electronic structure and the interaction between the impurities. We study these effects in the presence of both single and dual impurity potentials of varied strength using computational models based on tight-binding approach. We begin by looking at how the single impurity potentials affect the electronic properties of pristine graphene and gapped graphene. We analyze the change in DOS and energy of the system, along with the identification of the impurity states, utilizing participation ratio for localization. Then, we extend our study to dual impurity potentials and their impacts to provide a knowledge of multi-impurity scenarios. We explore the interaction of the impurities mediated by the Fermi sea. In particular, we studied the hybridization of impurity states and corresponding impurity energies. Next, we determine the force arising between impurities for various Fermi energies, impurity-impurity distances and impurity potential strengths for graphene and gapped graphene.