Darwin's theory of evolution by natural selection presented on his celebrated book On the Origin of Species is based on four main fundamental principles. These are:
Phenotypic variation deals with the individual variations amongst organisms' physical traits within the same species. These are differences in characteristics present in individuals of the same generation, that alter their corporal features.
The second postulate of Darwin's theory details that variations amongst organisms are heritable, meaning individuals can pass them down unto their offsprings.
Darwin also dealt with an issue he coined the "struggle for existence," which occurs when there are too many organisms in a population and the available natural resources can no longer support them. Nowadays, this phenomenon is referred to as overpopulation.
Within his book, Darwin also explained how heritable traits can affect organisms' survival and reproductive rates; traits that are favorable to a species are more likely to be passed on to future generations.
References
[CrashCourse]. (2012, Apr 30). Natural Selection - Crash Course Biology #14. [Video File]. Retrieved from https://www.youtube.com/watch?v=aTftyFboC_M