Why can all Turing machines be listed in a countable collection?

In automata theory, all Turing machines can be listed in a countable collection because each machine is defined by a finite set of instructions.1

A Turing machine operates based on a finite list of internal states and a finite alphabet of symbols. Its behavior is completely defined by a finite sequence of instructions, which can be represented as a finite list of quadruples or quintuples. Because every Turing machine can be described by such a finite, discrete string of symbols, the set of all possible Turing machines is equivalent to the set of all possible finite strings over a finite alphabet.1

In mathematics, the set of all finite strings over a finite alphabet is countably infinite. Consequently, because each machine corresponds to a unique, finite description, the collection of all such machines is also countable. This property allows for the existence of a "universal" machine, which can encode and simulate any other Turing machine by reading its finite instruction set from an input tape.1