Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation scheme which was introduced about three decades ago, but had yet to be implemented widely until recently. Most conventional communications systems send information sequentially over a channel. OFDM, however, allows information to be sent in parallel by the usage of orthogonal waveforms which do not interfere with one another. This allows multiple users to send information over the same channel simultaneously. Currently, OFDM is being used for Satellite Radio (XM Radio), Digital Video Broadcast (BBC), and will be used for fourth generation cellular networks. The OFDM architecture is based on the Fourier Transform and the results of Fourier analysis. In this thesis I explain the mathematics behind OFDM and design in Matlab based simulation to test the theory and examine the results.