This is the first fully comprehensive introduction to REDUCE - one of the most widely available and easy to use computing algebra packages around. Based on extensive teaching experience, it provides full coverage of REDUCE, from setting up to using user-contributed REDUCE packages written for specific applications. This will enable users to gain familiarity with the full range of REDUCE commands whilst simultaneously learning of the internal workings of REDUCE. Numerous exercises are provided throughout to illustrate themes covered in the text as well as to encourage `hands on' working with REDUCE. Everyone coming to REDUCE for the first time will find this an invaluable tutor and guide.