Things Fall Apart is one of the only books or plays that is both a tragedy of the individual and of the society. As you know, tragedy is structured for the downfall of the individual, while comedy is focused on exposing the pitfalls of society. Somehow, Achebe achieves both the aims of tragedy (focus on the individual) and comedy (focus on the society).
Achebe breaks the three Aristotelean unities (time, place, and action) in order to achieve this double movement. Achebe stages the novel using multiple settings, venues, and mistakes made by Okonkwo and the tribe. Most of all, he breaks the unity of time by stretching the novel across Okonkwo's years before exile, the seven years of exile, and Okonkwo's suicide. In a true Aristotelean tragedy like Oedipus, the author would begin at the end, near the death of the tragic hero (Part III of the novel), comprising his hamartia (flaw) and perepeteia (reversal). But, Achebe combines several mini-downfalls of the individual in preparation for the overall downfall of the tribe. Okonkwo's series of downfalls include the beating of his wife during the Week of Peace, the killing of Ikemefuna, the accidental shooting, the killing of the white messenger, and Okonkwo's suicide. Any of these might have been the basis for a shorter tragedy.
By narrating the novel from an objective, detached point-of-view, Achebe focuses also on the flaws of the society both with and without Okonkwo and before and after the colonists come. Focusing primarily on gender differences and pagan superstitions, Achebe exposes the flaws of the society that victimizes women, kills and exiles outcasts, overestimates the power of its gods, and underestimates the power of the white man's gods. Even Okonkwo, by the end, is angry at his own tribesmen for their weaknesses. Together, these flaws create a kind of dystopian effect on both the reader and the tragic hero.
First part: introduction of the Ibo people, of Okonkow and of his relatives. Introduction of their culture, religion, habits and beliefs.
The first part is here to make us discover (from the Ibo point of view) the daily life in their society, the way it was before the arrival of the white man. The story happens in Umuofia.
Second part: the seven years of exhile of Okonkwo inMbanta. We also hear about the arrival of the white men and see how they settle.
Third part: return to Umuofia. The white people have completely settled and they now rule the land.
The three parts represent in a way the history of the Ibo people: before the arrival (which covers a large period of time, this is why it is also the largest part in the novel), the setting of the white people and finally the new life under the reign of the white people.