One of the practical problems in digital communications is inter-symbol interference (ISI),which causes a given transmitted symbol to be distorted by other transmitted symbols. The ISI is imposed on the transmitted signal due to the band limiting effect of the practical channel and also due to the multi-path effects of the channel. The channel distortion may yield high error rate in symbol detection .One of the most commonly used techniques to compensate the channel distortion is linear channel equalization. More recently, there have been much interest in blind (self-recovering) channel equalization where no training sequences are available or used. In this thesis, we will discuss various equalization methods, including training based and blind methods. Of particular interest are the adaptation techniques. For this paper, computer simulations for blind equalization case is done verifying the validity of the theory. So, Godard family algorithm, an important class of adaptive blind channel equalization is implemented. As stochastic gradient descent in nature, they have practical computer implementation, but they have slowly initial convergence. Godard algorithms simulation results confirm better performance for constant modulus algorithm, CMA.