In this chapter, data compression as it relates to multimedia information is studied from the point of view of lossless algorithms, where the input data is essentially exactly recoverable from the compressed data Lossy algorithms, for which this is not the case, are presented in Chapter 8. Here we introduce the fundamentals of information theory and algorithms whose goal is a savings in bitrate given the entropy, especially Huffman Coding and its adaptive version. We then study Dictionary-based Coding (as in Winzip) and go on to a detailed discussion of Arithmetic Coding. Finally, Lossless Image Compression is examined specifically.