Galois fields are constantly gaining importance in quantum computing due to their wide usage in quantum error correction algorithms, and so it becomes relevant to define the QFT over Galois fields because of its main role in many of the most important quantum algorithms. The present article illustrates how to generalize the QFT so it can be applied over Galois fields and explains several examples of the application of the QFT over the simplest Galois fields. In particular the QFT will be defined for the Galois fields F2, F4 and GF(9), also the application of the QFT and the operations involved will be made using the Maple mathematical software.