  This paper presents a general and systematic discussion of various symbolic
representations of iterated maps through subshifts. We give a unified model for
all continuous maps on a metric space, by representing a map through a general
subshift over usually an uncountable alphabet. It is shown that at most the
second order representation is enough for a continuous map. In particular, it
is shown that the dynamics of one-dimensional continuous maps to a great extent
can be transformed to the study of subshift structure of a general symbolic
dynamics system. By introducing distillations, partial representations of some
general continuous maps are obtained. Finally, partitions and representations
of a class of discontinuous maps, piecewise continuous maps are discussed, and
as examples, a representation of the Gauss map via a full shift over a
countable alphabet and representations of interval exchange transformations as
subshifts of infinite type are given.
