The self-organizing map (SOM) is an unsupervised learning algorithm which has been successfully applied to various applications. One of advantages of SOM is it maintains an incremental property to handle data on the fly. In the last several decades, there have been variants of SOM used in many application domains. In this dissertation, two new SOM algorithms are developed for image quantization and compression. The first algorithm is a sample-size adaptive SOM algorithm that can be used for color quantization of images to adapt to the variations of network parameters and training sample size. The sweep size of neighborhood function is modulated by the size of the training data. In addition, the minimax distortion principle which is modulated by training sample size is used to search the winning neuron. Based on the sample-size adaptive self-organizing map, we use the sampling ratio of training data, rather than the conventional weight change between adjacent sweeps, as a stop criterion. As a result, it can significantly speed up the learning process. Experimental results show that the proposed sample-size adaptive SOM achieves much better PSNR quality, and smaller PSNR variation under various combinations of network parameters and image size. The second algorithm is a novel classified SOM method for edge preserving quantization of images using an adaptive subcodebook and weighted learning rate. The subcodebook sizes of two classes are automatically adjusted in training iterations based on modified partial distortions that can be estimated incrementally. The proposed weighted learning rate updates the neuron efficiently no matter of how large the weighting factor is. Experimental results show that the proposed classified SOM method achieves better quality of reconstructed edge blocks and more spread out codebook and incurs a significantly less computational cost as compared to the competing methods.