Karp's 21 NP-Complete Problems, introduced by Richard Karp in 1972, were the first set of problems proven to be NP-complete, establishing a foundation for the theory of computational complexity by demonstrating that a wide variety of combinatorial problems are computationally equivalent. This work was pivotal in understanding the boundaries of efficient computation, as it showed that if any one of these problems can be solved in polynomial time, all NP problems can be solved in polynomial time, implying P = NP.