Multiple-input-multiple-output (MIMO) communication systems are used to improve the signal quality, increase the data throughput and suppress interference. Unfortunately, multiple antennas cannot be mounted on small size terminals. To overcome this limitation, cooperative communication was developed. In this technique, all user terminals act as relays to assist a source terminal in transmitting information to the destination terminal, to form virtual multiple-input multiple-output (MIMO) systems. Applying space-time codes with cooperative approach, the resultant system is called distributed space-time code (DSTC). If the channel response change very fast, the well known differential space-time coding is needed. This eliminate the need for the channel state knowledge information at neither the relay nor the receiver, where each transmitted block acts as a reference for the next one. In this thesis, developing new low decoding complexity distributed differential space-time codes is considered. To achieve this, the idea of MIMO communication systems, differential space-time codes, low decoding complexity, cooperative communications and distributed differential space time codes will be studied. The developed codes are designed using circulant space-time codes. They work for networks with multiple number of two of relays, and have two-group decodable maximum likelihood receiver. The performance of the new code is analyzed via Matlab simulation which demonstrates that they outperform both Cyclic codes and Circulant codes.