What are the reasons for studying automata theory in a computer science?

There are several reasons to study of automata and complexity is an important part of the core of computer science.
1. Introduction to Finite Automata.
2. Structural Representation.
3. Automata and Complexity.

Introduction to Finite Automata: Finite automata are a useful model for any important kinds of hardware and software.
1. Software for designing and checking the behavior of digital circuits.
2. The “Lexical analyzer” of a typical compiler, that is, the compiler component that breaks the input text into logical units, such as identifiers, keywords, and punctuation.
3. Software for scanning large bodies of text, such as collections of Web pages, to find occurrences of words, phrases, or other patterns.
4. Software for everything systems of all types that has a finite number of distinct states, such as communications protocols or protocols for secure exchange of information.

Structural Representation:  
There are two important notations there are not automation-like, but play an important role in the study of automata and their applications
1. Grammars are useful models when software that processer data with a recursive structure.
2. Regular Expressions are denoted the structure of a data, especially text strings.

Automata and Complexity.
Automata are essential for the study of the limits of computation.
There are two important issues.
1. What can a computer do at all? This study is called “decidability”, and the problems that can be solved by computer are called “decidable”.
2. What can a computer do efficiently? This study is called “intractability,” and the problems that can be solved by a computer using no more time than some slowly growing function of the size of the input are called “tractable.” Often, we all polynomial functions to be “slowly growing”, while function that grows faster than any polynomial is deemed to grow too fast.