Image compression plays an important role in the storage and transmission of images. The demand for communication of multimedia data through the telecommunications network and access to multimedia data over the Internet is growing explosively. The image data comprises a significant portion of the multimedia data and occupies most of the communication bandwidth for multimedia communication. As a result, the development of "image compression" techniques for efficient image compression continues to be a major challenge for us both in academia and industry. We dedicate chapter 15 on the fundamentals of image compression. In this chapter, we present the theoretical bases of information behind data and image compression techniques, some source coding algorithms relevant to image compression standards and the principles behind image compression.