The Boolean Satisfiability Problem (often abbreviated as SAT) is a fundamental problem in computer science and mathematical logic. It involves determining whether there exists an assignment of truth values (true or false) to variables in a Boolean formula that makes the entire formula true. This problem is crucial in various fields, including artificial intelligence, hardware verification, and optimization. SAT is classified as an NP-complete problem, meaning that while it is easy to verify a given solution, finding that solution can be computationally challenging. The significance of SAT lies in its ability to represent many other problems, making it a central topic in the study of computational complexity and algorithms, particularly in relation to Karp's 21 NP-complete problems.