The usual theory of computation textbooks usually goes on to explain finite automata first, then context free grammar and finally the Turing machine. Why? Because the execution part of a TM is a finite automata, while the instructions can use the generative process of CFG. And then you got the whole computing world. Just from these principles (the other chapters are mostly about what's possible and what's not and exploration of other properties)

The nice thing about finite automata is that they can be composed together. That leads to a recursive pattern. This leads to the creation of higher abstractions, leading to general purposes CPU and special processors (gpu, npu, cryptographic chipset, hardware encoding,...). The same things applied to CFGs lead to the creation of programming languages.