I've just finished reading Fathers and Sons (written in 1861), and have compiled a few short portions of the book. I believe these are the main points which Turgenev is trying to communicate to his reader. If you read what I have provided for you here, you'll get a good idea of what Fathers and Sons focuses on, without having to read all of the plot's detail. These are very meaningful passages, both for Turgenev's era and for ours. They discuss conflicting ideas, and the battle of ideas is the unceasing struggle of humanity.
Bazarov and Pavel Petrovich's Dispute: The Nihilist's Introduction
Bazarov and Anna Sergeyevna's Dispute: A Nihilist's Dream
Bazarov's Confession: A Nihilist's Angst
Bazarov Declares All is Subjective: A Nihilist's Description of Reality