The continuous growth of demand on internet requires high speed connection and larger capacity on telecommunication networks. In order to satisfy the day-by-day increasing connection requests, a new modulation technique named Orthogonal Frequency Division Multiplexing (OFDM), which promises faster connection and better usage of optical spectrum has been developed in optical networks. In this thesis, we propose solution methods for the Routing and Spectrum Allocation problem that has emerged with the adaptation of OFDM technology. Our goal is to find the minimum amount of spectrum slots that can be used while routing connection requests from their source to destination and allocating an adequate spectrum to the signals. We provide a new integer linear programming formulation for RSA and an improved formulation for the RSA problem with a predefined set of paths. We also propose two heuristic algorithms, Least Cost Slot Allocation and Iterative Common Path Allocation, and provide computational tests to illustrate the performance of our ILP model and heuristic algorithms.