Population genetics is a branch of biological studies. Population geneticists study the genetic composition of a given population and study the changes in genetic composition in that population that result from various factors. One of those factors is natural selection, so population genetics is heavily influenced by Darwin and his ideas about adaptation, fitness levels, and natural selection.
Additionally, population genetics encompasses work that was founded by Mendel. Darwin said that a species could change over a period of time. He knew that within any given species, variation existed. These random changes would cause some individual organisms to have adaptations that allowed them to better survive current environmental factors. These adaptations allowed an organism to be more fit, and more fit organisms tended to survive more often, hence "survival of the fittest." The fit, surviving individuals were more likely to reproduce and pass on their trait. Given enough time that trait could become widely spread through an entire population.
What Darwin didn't know was what was being passed on from generation to generation. He didn't know what was causing the random adaptations. This is where Mendelian genetics comes into play. Mendel's work led to knowledge about genes, alleles, and issues of dominance regarding those traits. Population genetics as a scientific field came about in the early part of the 1900s through the work of Fisher, Haldane, and Wright. Their work showed that Mendelian genetics and Darwinian natural selection integrated quite well together.