In popular usage, "the" theory of evolution refers to the various theories proposed by Charles Darwin, notably the theory of common descent, and the theory of evolution by natural selection. It also refers to the modern Darwinian theory that combines evolutionary theory with the science of genetics.
Natural selection suggests that a species has the ability to adapt to changes in the environment, by random genetic mutations that occur.
Huh? That seems to be an error. If the mutations are randomly caused by cosmic rays, this seems to be an environmental factor rather than an ability.
These mutations can alter the individual's physical shape or the inner workings of the body so that organs may change their shape or size or the immune system may develop a different reaction towards disease. After the mutation has occurred, it's up to nature to test that change in real life. If the change benefits the individual, the individual is most likely to have a better chance of survival. Otherwise, the individual will most likely die and the faulty mutation will be discarded. Often these processes last thousands of years due to the slow rate of mutations as well as the lifespan of the individual, although it seems that in some cases evolution can occur unbelievably quickly, within a few generations (Punctuated Equilibrium). /Talk1
Evolution by natural selection has been observed so many times that it is now considered a fact. There have been numerous observed cases of speciation, especially in plants (see [link] for more details). Speciation has not been observed per se in vertebrates?, although there are numerous examples of no-longer breeding subpopulations.
Important concepts in evolution: