  Gauge invariance in discrete dynamical systems and its connection with
quantization are considered. For a complete description of gauge symmetries of
a system we construct explicitly a class of groups unifying in a natural way
the space and internal symmetries. We describe the main features of the gauge
principle relevant to the discrete and finite background. Assuming that
continuous phenomena are approximations of more fundamental discrete processes,
we discuss -- with the help of a simple illustration -- relations between such
processes and their continuous approximations. We propose an approach to
introduce quantum structures in discrete systems, based on finite gauge groups.
In this approach quantization can be interpreted as introduction of gauge
connection of a special kind. We illustrate our approach to quantization by a
simple model and suggest generalization of this model. One of the main tools
for our study is a program written in C.
