Abstarct: In this dissertation, we describe some aspects of quantum field theory in the background space-time created by some linear topological defects. Inspired by the descxription of linear topological defects in crystalline solids, we construct a generalization of this topological defect in gravitation. The dissertation is divided into seven chapters, first of all, in the introduction chapter, we indicate how the rules of coordinate transformations for vectors, tensors, and spinors in a non-flat spacetime background obey the rules established in general relativity. In the second chapter, we introduce some kinds of background space-times generated by linear topological defects. In the third chapter, in the context of the investigation of non-relativistic systems under the background produced by topological defects, we consider a moving particle with a magnetic quadrupole moment in an elastic medium in the presence of a disclination and screw dislocation. We assume a radial electric field in a rotating frxame that leads a uniform effective magnetic field perpendicular to the plane of motion. We solve the Schrödinger equation to derive wave and energy eigenvalue functions by employing analytical methods for a static scalar potential. In the fourth chapter, we first answer the question of how to incorporate spinor and scalar fields into general relativity. Hence, we present the generalized Dirac, DKP, and Klein-Gordon equation in the non-flat space-time. In this way, we define fields in the local reference frxame of the observers as well as build a local reference frxame for observers. In the fifth, sixth, and seventh chapters the influence of space-time background generated by topological defects on the fermionic and bosonic systems in the presence of a relativistic quantum oscillator, a spin symmetry limit, a pseudospin symmetry limit, and a Lorentz symmetry violation scenario are investigated. Besides, we use various analytical methods to find exact solutions to the generalized relativistic equations of motion in the geometric background.