The polymerase chain reaction (PCR) has become a standard laboratory technique. An enzymatic reaction, as simple to perform as it is satisfying to contemplate, the PCR solves two of the more universal problems in the chemistry of natural nucleic acids. It allows for the physical separation any particular sequence of interest from its context; and then provides for an in vitro amplification of this sequence which is virtually without limit. The surprising robustness of PCR derives from its fortuitous combination of three phenomena, each of which is intrinsically powerful. The first of these is the impressive ability of almost all oligodeoxynucleotides to bind tightly and specifically to their complementary nucleic acid sequences, discriminating easily between hundreds of thousands of sites. The second familiar phenomenon is illustrated by the notion that the probability for the occurrence of a compound action is the product of the individual probabilities for the occurrence of each of its components. The third phenomenon embodied in the polymerase chain reaction relates to the branching structure of its propagation and the inherent robustness attached to such a form. Consideration of the above leads to certain generalities regarding the relative utility of various protocols for carrying out the PCR. Specific conditions of time, temperatures, concentrations, etc. will be described, as well as sample preparation and analytical methods.