I apologize for the confusion, but there is no specific "Cook's Theorem" in the theory of computation. However, there is a well-known result called "Cook's Theorem" or "Cook-Levin Theorem" that is fundamental in the field of computational complexity theory.
Cook's Theorem, proven by Stephen Cook in 1971, states that the Boolean satisfiability problem (often referred to as SAT) is NP-complete. The SAT problem involves determining whether there exists an assignment of truth values to variables in a Boolean formula that makes the formula evaluate to true. NP-complete is a class of computational problems that are considered the hardest problems in the class NP (nondeterministic polynomial time).
Cook's Theorem has significant implications for the theory of computation. It demonstrates that if a problem is NP-complete, then it is computationally difficult to solve, in the sense that there is no known efficient algorithm to solve all instances of the problem. Furthermore, any problem in the class NP can be reduced to SAT in polynomial time, which means that if one can efficiently solve SAT, then all NP problems can be efficiently solved as well.
The notion of NP-completeness and Cook's Theorem laid the foundation for the study of computational complexity and the identification of many other NP-complete problems across various domains. It provided insights into the inherent difficulty of certain computational tasks and the relationships between different problems in terms of their computational complexity.