The novel is set in a Russian provincial town and deals with the events surrounding the Karamazov family and the complex relationships between the father and his sons.
The narrative can be divided into three fundamental parts.
In the first part, the profiles of the main characters are outlined through a succession of dramatic events, in which the sons' feelings toward their father are revealed (contempt and hatred, but also the awareness of being "cut from the same cloth"), and thereby the complex, contradictory temperaments of the protagonists: Dmitri, impulsive and "animalistic," yet also swept away by passion and love; Ivan, cynical and reflective, yet also anguished by a profound sense of guilt and despair (over the suffering of humanity and the consciousness of being like his father); Alyosha, good and gentle, yet in a sense a bystander to the dramatic events and himself gripped by a sensuality inherited from his father; and finally the old Karamazov's illegitimate son, Smerdyakov, who embodies all the pain, the sense of injustice, and the hatred also present in the brothers, but in an "animalistic" and therefore unrestrained dimension.
The first part of the novel, the richest in themes and resonances, depicts the philosophical and religious world of the narrative, in the extensive treatment of Father Zosima (his worldview, his death, and the disillusionment over the rapid decomposition of his corpse), and then in the dialogue between Ivan and Alyosha (the chapters Rebellion and The Grand Inquisitor).
In the second part, the events leading to the murder of old Karamazov and the arrest of Dmitri are depicted.
These are the most fragile chapters of the book, centered primarily on the figure of Dmitri and on two female characters: Katerina Ivanovna (Dmitri's fiancée, who nevertheless loves Ivan) and Grushenka, the woman who provides the ostensible motive for the crime (Dmitri loves Grushenka, who is in turn coveted by old Karamazov).
The second part concludes with the mutual acknowledgment of love between Dmitri and Grushenka.
The third part describes the trial, with the closing arguments of the prosecutor and the defense counsel.
Yet the true focus of this part lies in the encounter between Ivan and Smerdyakov, and in the latter’s accusation against Ivan: Smerdyakov murdered old Karamazov because he felt sanctioned by Ivan’s departure.
In truth, Ivan is the real instigator of the crime.
This revelation gives rise to Ivan's descent into madness and, in a sense, to Katerina's decision to present in court a letter from Dmitri foreshadowing the murder, which will form the basis of the conviction.
Critics typically speak of two levels on which the characters should be "read": the empirical and the metaphysical.
In truth, one should also distinguish between the metaphysical-religious level and the metaphysical-philosophical one.
From the "empirical" point of view, the rhythm of the narrative rests essentially on dialogue between the characters and is embodied in the theme of the contradiction between rationality and irrationality: the characters appear driven by two conflicting forces, yet are continually brought back to a "destiny" grounded in the intrinsic nature (in their genetic code, as one might say today) of the individual.
This is the plight of the Karamazov brothers: they hate and despise their father, or take pity on him (in Alyosha's case), but in every instance they are forged from the very same nature, to which they are irremediably bound.
This ineluctability of their nature is clear to Ivan (and lies at the root of his madness); it is conspicuous in Dmitri and Smerdyakov, yet it also surfaces in Alyosha, for instance in his dealings with young Kolya.
As Ivan says in a conversation with Alyosha:

why lie to oneself, when all men live like this and perhaps cannot live otherwise? Are you asking me this on account of what I said just now, that one reptile will inevitably devour the other? Allow me then, in that case, to ask you a question: do you believe me capable, like Dmitri, of shedding Aesop's blood—that is, of killing him?

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The second level is the religious one, which is deeply intertwined with the theme of suffering and its compatibility with the existence of God.
As Ivan says to Alyosha in the chapter Rebellion:

if all must suffer in order to purchase eternal harmony with suffering, what have children to do with it?...
I do not want harmony; I do not want it out of love for humanity...
It is not that I do not accept God, Alyosha: I simply, most respectfully, return Him the ticket.
If the sufferings of children have gone to replenish the sum of suffering needed to pay for the truth, I declare right now that no truth is worth such a price

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There is no certainty in faith; Alyosha himself doubts the very moment he witnesses the decomposition of Father Zosima’s body, and, above all, God cannot be justified if such suffering exists in the world.
The third level is the philosophical one, bound to the rise of modern man.
It is in the chapter of The Grand Inquisitor that the conflict is articulated between Christ's sacrifice to grant men freedom of judgment and the desire of the Church (and thus of any Institution) to keep men in a state of tutelage.
Thus speaks the Grand Inquisitor:

what fault is it of the weak soul if it lacks the strength to receive such terrible gifts?...
And if there is a mystery, we too had the right to preach mystery and teach men that it is not the free choice of their hearts that matters, nor even love, but mystery, to which they must bow blindly, even against their conscience.
And so we have done.
We have corrected Thy work and founded it upon miracle, mystery, and authority

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The link between the three levels (empirical, religious, and philosophical) is forged by Ivan's assertion that everything is possible for man: this articulates a concept of the "man without limits" that lies at the root of all the novel's events, its philosophical framework, and the contradictions present within the characters and the spirit that animates the book.

The Brothers Karamazov