A polymer is a very-long-chain macromolecule in which hundreds or thousands of atoms are linked together to form a one-dimensional array. The skeletal atoms usually bear side groups, often two in number, which can be as small as hydrogen, chlorine, or fluorine atoms or as large as aryl or long-chain alkyl units. Polymers are different from other molecules because the long-chain character allows the chains to become entangled in solution or in the solid state or, for specific macromolecular structures, to become lined up in regular arrays in the solid state. These molecular characteristics give rise to solid-state materials properties, such as strength, elasticity, fiber-forming qualities, or film-forming properties, that are not found for small molecule systems. The molecular weights of polymers are normally so high that, for all practical purposes, they are nonvolatile. These characteristics underlie the widespread use of polymers in all aspects of modern technology. Attempts to understand the relationship between the macromolecular structure and the unusual properties characterize much of the fundamental science in this field. Polymers are among the most complicated molecules known. They may contain thousands of atoms in the main chain, plus complex clusters of atoms that form the side groups attached to the skeletal units. How, then, can we depict such molecules in a manner that is easy to comprehend? First, an enormous simplification can be achieved if we remember that most synthetic polymers contain a fairly simple structure that repeats over and over down the chain. This simplest repetitive structure is known as the repeating unit, and it provides the basis for an uncomplicated representation of the structure of the whole polymer. For example, suppose that a polymer consists of a long chain of atoms of type A, to which are attached side groups, R. The polymer chain can be represented by the formula shown in 1.1. The two horizontal lines represent the bonds of the main chain. The brackets (or parentheses) indicate that the structure repeats many times. The actual number of repeating units present is normally not specified, but is represented by the subscript, n.