Small changes in a system are called perturbations. In a straightforward perturbation computation, two independent simulations are performed and the difference of the two results are calculated. This type of approach, using Monte Carlo methods, can be inefficient and even impossible to solve in some cases. For small perturbations, the relative error of the difference of two independent simulations can be much larger than the relative error of the unperturbed or perturbed quantity [Spa69]. Hence, it is necessary to employ special Monte Carlo techniques that calculate the difference of two responses, independent of their statistical uncertainties. These Monte Carlo perturbation techniques include correlated tracking, derivative operator sampling, the importance function approach [Rie86, Lux91] and the linear perturbation theory [Bel70] approach. The linear perturbation theory requires information about the angular neutron flux and hence has not been studied in this work. These other three methods employ different estimators and their uncertainties may differ considerably, depending on the problem tested. The first two methods may be applied to reaction rate perturbation calculations as well as eigenvalue perturbation calculations. The importance function approach is mainly used for eigenvalue perturbation calculations. The usual source iteration method for Monte Carlo eigenvalue calculations encounters difficulty, due to the propagation of perturbed weights from one generation to the next [Rie84, Spa69]. To avoid this difficulty, an adjoint function must be used, and this gives rise to the importance function approach for eigenvalue perturbation calculations. For eigenvalue perturbation calculations, using correlated and derivative operator sampling, these two methods are applied to the Green's function or fission matrix approach for eigenvalue calculations. In the fission matrix approach, the homogeneous neutron transport equation is first discretized by subdividing the fissionable region into a mesh of volume elements. Next, a random walk simulation is done to estimate the elements of the fission matrix that contains the mutual fission probabilities for these volume elements. The dominant eigenvalue of this fission matrix gives the multiplication factor of the system. In this thesis work we have combined the correlated sampling technique and the fission matrix method to calculate multiple eigenvalue perturbations from a single Monte Carlo simulation. Below, we briefly explain the correlated tracking, derivative operator sampling, and the importance function approach.