The basic ideas of Darwin’s The Origin of Species (1859) are that of the tree of life and of natural selection.

Tree of life: living organisms are organized as the limbs of a great tree, with more general groups branching into lesss general ones. Moreover:

1. species change over time (transmutation)
2. some species go extinct (extinction)
3. some species keep diverging, splitting eventually into multiple descendent species (common descent).

NOTE:extinction and common descent are not necessary for transmutation. For example, Lamark rejected extinction and common descent (species don't split).

Natural Selection is the principal mechanism for descent with modifications (evolution). For Darwin, its existence can be established by considering the following:

First Fact: The Struggle for Existence

• intraspecific: two canids struggling for scarce food; several mistletoes parasitizing the same tree and trying to attract birds to disseminate their seeds, etc.
  
• interspecific: the same mistletoes competing with other fruit bearing plants; a plant’s seed germinating in a crowds field, etc.
  
• environmental: a plant at the edge of the desert struggling against drought, etc.
  

NOTES:
In equatorial areas, the struggles is mostly intra and inter-specific, while in hostile environments (e.g., Arctic regions, or high mountains) the competition is mostly environmental.
Intrageneric struggle is very intense because species of the same genus are close in structure and often in habits. This is the basis for the Principle of Divergence, by which the more diversified the descendants from one species become, the more successful they’ll be.

• an annual plant producing only 2 seeds a year will have 2ⁿ descendants in n years. In general, organisms tend to increase in geometric ratios.
  

domestic animals run wild in new environments often have population explosions.


Second Fact: Individual Natural Variation and Its Transmissibility to Progeny
This is evidenced in the selection of breeders concerning plants and animals (dogs, cats, pigeons).
NOTE: as to the mechanism of variation and transmission, D. is silent in The Origin. However, in The Variation of Animals and Plants under Domestication (1868) he adopts pangenesis (gemmulae and quasi-Lamarckism)
Importance of cross pollination (the mixing of traits from the parents).

Struggle for existence plus individual natural variation and transmissibility to progeny produce Natural Selection, the mechanism of evolution. Natural selection consists in the preservation of favorable variations and the elimination of injurious ones, while neutral variations are left fluctuating. Darwin give a famous metaphor for natural selection: “The face of Nature may be compared to a yielding surface, with ten thousand sharp wedges packed close together and driven inwards by incessant blows, sometimes one wedge being struck, and then another with greater force.”
The result of natural selection is Evolution (descent with modifications). Species, then are just “strongly marked and permanent varieties.”
All animals descend from four or five projenitors, and so do plants; moreover, given the similarities between plants and animals (e.g., in their reproductive processes) it’s not absurd to believe that all life may descend from a common origin.

In the final chapter of his book, Darwin considers the main objections against descent with modifications; here are some:

• How could complex organs be the product of evolution?
  

Answer: They can be result of small modifications, each favorable, through a very long period of time. Example, eye starting with nerves which are light sensitive. This addresses the issue of irreducible complexity (the all or nothing objection) advanced by Paley with respect to the eye.
NOTE: In his study of orchids (1862) D. also notes that their various reproductive contrivances for attracting insects are formed out of pre-existing material (typically petals).
In addition, often organs are not contrivances but contraptions (Gould’s panda’s thumb).

• How can different species descending from on parent have become so geographically separated?
  

Answer: we don’t know of the climatic and geographical changes which may have facilitated migration or brought about the extinction of a species in the intermediate region.

• How come we don’t observe intermediate forms all around us? Why are not all organic being blended together in an inextricable chaos?
  

Answer: Intermediate forms existed not between existing forms, but between each existing form and some extinct one. Moreover, the Principle of Divergence tells us that intermediate forms are tend to become extinct.

• Why doesn’t the geological record show the innumerable intermediate forms between the present ones and other extinct ones?
  

Answer: the geological record is sorely incomplete. In addition, the principle of Divergence tells us that the intermediate species become extinct quickly.

• Forms of life are arranged in few great classes and in groups subordinate to groups. The theory of species creation is unable to explain this fact. By contrast, the principle of divergence explains the tendency of large groups to increase in size and diverge in character,
  
• The principle of divergence also explains the extinction of older intermediate varieties, and therefore gives an account of the fossil record, incomplete as it is.
  
• Cases of want of perfection involving vestigial or rudimentary organs/features: upland geese which almost never swim have webbed feet; thrushes that dive and feed on sub-aquatic insects; the sting of bees causing their own deaths; occasional horses with stripes on their legs and shoulders etc.; at times organs are badly designed, more contractions than contrivances. Species creation cannot explain this, while evolution can.
  
• Interspecific breeding (e.g. horse/donkey) follows the same inheritance laws as intraspecific breeding (varieties of same species). This is explained by species being not essentially different from varieties. But for creationism, species are independently created while varieties are produced by secondary laws, so that the two are essentially different.
  
• Oceanic islands are occupied by few species, but often with peculiar subspecies. Divergence explains this, while separate creation does not.
  
• Homology: the bone structure is the same in hand of man, fin of porpoise, wing of bat, and leg of horse. Descent with modification explain this, but separate creation does not.
  
• Embryos of a fish, bird, mammal are very much alike even if the adults are not (e.g., embryos of mammals deveop a 2 chamber heart, like fish). Descent with modification explain this, but separate creation does not.
  

• There was no sense of deep time
  
• the geological record has been taken to be complete, and it doesn’t show the insensible variaations from extinct species to present ones.
  
• We are slow in admitting great changes of which we don’t see the steps. But Lyell has disabused us of this prejudice.
  

Darwin ends his book with the famous tangled bank metaphor:

"It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms. Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved."

In The Descent of Man (1871), Darwin applies natural selection to our own species. Two main points are notable:

• Sexual Selection. Introduced in the second part of Descent, to account for features like the peacok tail (large tails directly favored by females) or deer antlers (competition with other males in order to get females)
  
• Origin of Man: In The Origin, D. had merely stated that his theory might shed some light about the orign of man. In the first part of Descent he tried to make good on his claim. The procedure is predictible: morphologically, we are quite similar to the great apes; as Huxley noted, the foot of the gorilla is closer to ours thatn to that of the orongutan’s. the real problem has to do with higher functions (e.g. intelligence) and their manifestations, e.g., moral behavior, religious beliefs, etc. His explanation was that religious beliefs favor the sense of remorse, which in turn supprts morality, which in turn favors the group, and indirectly the individual (groups without any moral sense cannot survive for long).