Digital compression of audio data is important due to the bandwidth and storage limitations inherent in networks and computers. Algorithms based on perceptual coding are effective and have become feasible with faster computers. The ISO standard 11172-3 MPEG-1 layer III (a.k.a. MP3) is a perceptual codec that is presently very common for compression of CD quality music. An MP3 decoder has a complex structure and is computationally demanding. The purpose of this master's thesis is to present a tutorial on the standard. We have analysed several algorithms suitable for implementing an MP3 decoder, their advantages and disadvantages with respect to speed, memory demands and implementation complexity. We have also designed and implemented a portable reference MP3 decoder in C.