A polymer is a molecule composed of a small molecular unit repeating in a chain; usually units. The chain may have complicated topology, like branches, or cross-links. Links can also be made between different polymers (of different chemical composition for instance). These all determine the polymer architecture.
Polymer chemistry
Example of polymer: https://en.wikipedia.org/wiki/Polystyrene
Main architectures:
More specific examples of architectures:
Interestingly, when one closes a linear-chain polymer into a loop, the viscosity drops dramatically.
Addtion polymers created by Addition reactions
Alkenes can act as monomers because they are unsaturated:
Condensation polymers created by Condensation reaction
An example of a condensation polymer is nylon, and some Proteins (the ones that are formed from repeating units)