List the two elements of darwin’s theory of evolution. what are some objections to these concepts?

The two main points from Darwin's theory of evolution is that 1) most, if not all living organisms evolved from  one or just a few common ancestors and that subsequent specialization of further generations then led to new species. Furthermore, he said that 2) the process how this was done was by natural selection where the organisms which were most adapted to their environment were successfully 'remembered in the gene pool'.