Image compression is the process of reducing the required amount to represent an image and one of the most powerful and useful technique of digital image processing. Here in this paper we have discussed some fundamental concepts behind image compression techniques and apply wavelet transform for the compression of images. Wavelet transform is the most popular transform of time frequency signals. In this paper wavelets – haar, daubechies, biorthogonal and coiflet of wavelet families are used for compression. A comparative study is also done by Peak signal to noise ratio (PSNR), Mean square error (MSE), Compression Ratio (CR) etc. quality measuring parameters of images.