It is known that a digital image requires large number of bits for its representation thereby occupying huge memory in the storage device. Also, the time of transmission of such an image is considerable. The storage space, transmission time and the transmission bandwidth requirements of an image can be considerably reduced by using image compression techniques. Image compression converts an input raw digital image into an output binary data stream that has smaller size than the input digital image. Image compression techniques are classified into two categories, namely lossless and lossy. In this book, four new image compression algorithms are proposed for compressing gray scale images.