The \(\textsf{NP}\) -complete problems are hardest problems in \(\textsf{NP}\) , so far no algorithm has been found for any of the \(\textsf{NP}\) -complete problems. But, due to their existence in many practical applications, their efficient solution carries a lot of significance. The interesting fact about all of them is that if any one of the \(\textsf{NP}\) -complete (NPC) problem is found to have a polynomial solution, all the NPC problems will have polynomial solution. One way to have an efficient solution to a problem is to reduce it into some simpler problem. The above are the topics of this chapter, in addition, it presents some of the standard \(\textsf{NP}\) problems to begin with, gives a more detailed deliberation about Satisfiability (SAT) problem, and shows that SAT is in \(\textsf{NP}\) . Next, the Cook–Levin theorem proves that SAT is in \(\textsf{NP}\) -complete, this is followed with various proofs about \(\textsf{NP}\) -complete, and introduction to number of \(\textsf{NP}\) -complete problems. Various approaches are presented about how to solve SAT problem. In the end, counting problems are introduced with their significance and their fields of applications, followed by self-review questions and exercises.