The opening line is quite familiar: "Happy families are all alike, every unhappy family is unhappy in it's own way".
The last line, less famous, is a thought from Levin (one of the main characters) who has experienced something of an epiphany ... "I shall still be unable to to understand with my reason why I pray, and I shall go on praying; but my life now, my whole life apart from anything that can happen to me, every minute of it is no more meaningless, as it was before, but has the positive meaning of goodness, which I have the power to put into it."
From a Christian perspective, his epiphany fell a bit short -- and there are some lines in the book that would indicate that at one level "he" (Tolstoy) does know that he actually doesn't have the "power" -- meaning/purpose is a gift from God.
I made it through it! It is pretty much a romance novel writ large. An easy summary of the book would be "adultery often doesn't work out well". (like one participant "takes a shot" at killing himself, and the other is more successful -- trains are effective! I'm certain that modern "progressive" moralists would argue that it was the rigid social rules that caused the derailment, however "if it feels good do it" as a moral foundation doesn't seem to be working out that well either based on depression, suicide rates and addiction.
One reason that the book is revered is the EXTENSIVE and DETAILED interior thoughts of the characters. Having read one romance novel early in my marriage, and realizing that the alleged interior of the female mind was not likely to be of use to me (other than realizing"it's hopeless") , it does seem that Tolstoy had some insight into this terra incognita. (note my ability to extrapolate a "rule" from a SINGLE "Danielle Steele" book read 35 years ago)
At least for me, a good deal of a tug -- but then I've always known I'm an uncultured lout!