FORM is a system that tries to use the computer resources as efficiently as possible, while at the same time trying to be as general as possible. Its internal representations are far more compact than those of the popular Computer Algebra Systems (CAS), but at the same time this has not been overdone as speed of processing is the major optimization criterion. What is special about it is that formulas can be disk based without big penalties in the performance. This means that the available diskspace puts the practical limits on the size of expressions, rather than the amount of RAM memory.
FORM is not just a faster version of the popular Computer Algebra Systems (CAS): its programming model is completely different. For some people there may be an initial threshhold, but once this is passed the language is experienced as rather logical and natural. Very often people use both a CAS and FORM and create hybrid programs that move formulas between them. This way complicated problems both in physics and in mathematics have been solved.
FORM is extremely fast compared to competitors like Mathematica and Maple. Parallel processing is used intensively.
FORM has been used to solve complex problems ranging from high energy physics to mathematics.
FORM is open-source and free to use for anyone. Contributions are of course welcome.