How we cite our quotes: (Part.Chapter.Paragraph), with the exception of Part V, which runs (Part#. "Short Title". Paragraph). Part V has no numbered chapters—only title headings.
Quote #1
He imagined putting into this landscape...Mrs. Nora's naked body, and the thought then came to him that beauty is a spark that flashes when, suddenly, across the distance of years, two ages meet. That beauty is an abolition of chronology and a rebellion against time. (II.13.17)
Karel enters into an elaborate fantasy world in which he can overcome the distance of many years to make love to Mrs. Nora, his mom's beautiful friend that he met as a young child. He senses that this imaginative action will somehow right an injustice of chronology (i.e., that at a young age, he couldn't make love with a sexy lady) and finally quench his insatiable sexual desire.
Karel gets so carried away with this idea that the very actions of love feel like violations of the space-time continuum, allowing him to have sex not only with Eva (who's actually there), but also with the distant (and probably dead) Mrs. Nora.
Quote #2
Just as someone in pain is linked by his groans to the present moment (and is entirely outside past and future), so someone bursting out in such ecstatic laughter is without memory and without desire, for he is emitting his shout into the world's present moment and wishes to know only that. (III.2.5)
Kundera finds that humans live completely in the present on either end of the happiness spectrum; total misery and ecstatic happiness ground us to our place in time. Both of these states of being carry little psychological or historical weight, since we're entirely absorbed in the intensity of the moment. That's heavy, bro.
Quote #3
The only amusing thing about it all was my existence, the existence of a man erased from history, from literary histories, and from the telephone book, of a dead man now returned to life in an amazing reincarnation to preach the great truth of astrology to hundreds of thousands of young people in a socialist country. (III.3.5)
Kundera talks about his short-lived gig as an anonymous astrology column writer in Czechoslovakia. He's been dissed by the Communist regime and has lost his social and professional standing, which leaves him a bit short of cash, so a faithful young friend helps him out with the job. Despite his bitter disappointment, Kundera sees the cosmic irony in the whole tragic situation: he's selling superstitious nonsense to people who claim to be skeptics.