"Ah, what a destructive creature is man...How many different plant-lives he destroys to support his own existence!"
The opening of the novel is essentially just the story of the narrator finding a red thistle in a field, marveling at its resilience, beauty and strength after being bent and covered in mud. This quote in particular is Tolstoy's musing on two of the major themes of the novel--violence and war. Tolstoy uses "plant-lives" as a metaphor for the actual human lives we destroy during war. Man as a destructive creature is central to the meaning of the novel, as little is actually achieved in the story save violence and destruction.
"23rd Nov.--Two companies of the Kurin regiment advanced from the fort on a wood-felling expedition. At mid-day a considerable number of mountaineers suddenly attacked the wood-fellers. The sharpshooters began to retreat, but the 2nd Company charged with the bayonet and overthrew the mountaineers. In this affair two privates were slightly wounded and one killed. The mountaineers lost about a hundred men killed and wounded."
This letter is written by Poltoratsky to the Russian command in Tiflis after Adveev's death. Tolstoy uses this letter to highlight the absurdity of Adveev's death: he was killed not in a planned military conflict, but while doing the unnecessary task of chopping wood in the forest. Tolstoy intends for the reader to view Adveev's death as a tragedy as evidenced by the chapter-long exploration of his selflessness. The wasteful nature of his death is heightened by the flippant description of the deaths of 100 Chechens. The deaths of Adveev and these Chechen fighters are reduced to numbers, highlighting the impersonality of war and massive waste of human life.
"My white bosom was pierced by the blade of bright steel,
But I laid my bright sun, my dear boy, close upon it,
Till his body was bathed in the stream of my blood.
And the wound healed without aid of herbs or of grass.
As I feared not death, so my boy will ne'er fear it."
Hadji tells the story of his father stabbing his mother for refusing to wet-nurse the son of the Khan to Loris-Melikov, who asked for Hadji's life story. She sang this son to Hadji as a child, which is extremely telling towards his own view of struggle. She, like her son, was hurt and beaten down, but remains incredibly resilient. This story was likely a significant moment in Hadji's life, as it gave him courage over death and the incredible durability that defines him in the face of hardship. Her assertion that her wound healed without "aid of herbs or of grass" explains why her son has a preference for solving his own problems, offering a reason behind his reluctance to allow help from the Russians.
"Yet though convinced he had acted rightly, some kind of unpleasant after-taste remained, and to stifle that feeling he dwelt on a thought that always tranquilized him--the thought of his own greatness."
Nicholas I is depicted as a tyrannical, lazy adulterer in the novel, and offers this quote after he has just cheated on both his wife and his mistress with a 20 year old Swedish girl. He admits to feeling mildly guilty--the "unpleasant after-taste"--and dissolves the feeling by focusing on his greatness and perfection. Nicholas is a classic narcissist, and mentions several times that he is a wonderful gift to the world. His dalliances with young beautiful women who profess to adore him (but who likely just agree to sexual affairs with him out of fear) encapsulates his bloated self-image. It is this self-image that propels him to be careless with the lives of his troops; he assuages any guilt he feels by focusing on himself.