Chapter 1 is simple one in which Farmer Gabriel Oak and Bathsheba are both introduced to us and are simultaneously introduced to each other, or rather, Oak witnesses Bathsheba's actions and is thus introduced to her while Bathsheba is aware of no one but herself, a telling characteristic that carries through the whole novel as self-absorbed vanity.
Oak: His Christian name was Gabriel, and on working days he was a young man of sound judgment, easy motions, proper dress, and general good character.
Bathsheba: The picture was a delicate one. ... She simply observed herself as a fair product of Nature in the feminine kind, her thoughts seeming to glide into far-off though likely dramas in which men would play a part ....
Chapter 2 introduces us into Oak's life and informs us of some of his superior traits like his musical abilities and his knowledge of the stars in the heavens: "since evening the Bear had swung round it outwardly to the east, till he was now at a right angle with the meridian." This leads to his night of helping his flock to bring lambs into the world, a night of building and tending his flock: "bringing in his arms a new-born lamb." Then he finds himself in a second observation of Bathsheba from afar as she and her aunt tend to Daisy, their cow. Oak discovers the adventurer in Bathsheba as she rides off without a lady's sidesaddle.
"Yes, aunt; and I'll ride over for it as soon as it is light." "But there's no side-saddle." "I can ride on the other: trust me."
In Chapter 3 Bathsheba's steadier and better qualities, like modesty without shyness, are described and she and Oak have a face-to-face meeting and conversation.
"[The hat] is mine." said she, ... "it flew away last night." "One o'clock this morning?" "Well — it was." She was surprised. "How did you know?" she said. "I was here." "You are Farmer Oak, are you not?"
More importantly, Bathsheba saves Oak from carbon monoxide poisoning in his shepherd's shed by throwing milk ("as there was no water") on him and ventilating the place. This act of life-saving, facilitated by Oak's dog dragging her from Daisy's shed to Oak's hut, leads to more conversation and Oak's love.
The young girl with the remarkably pleasant lips and white teeth was beside him. More than this — astonishingly more — his head was upon her lap,
Chapter 4 finds Oak resolved to marry Bathsheba. He goes to her aunt's cottage. Her aunt tells a fib to Oak saying that, yes, Bathsheba has many suitors, thus sending Oak away without talking to Bathsheba herself. Learning of this, Bathsheba runs down the country lane to catch him only to say that she has no other suitors but nonetheless cannot marry him because he is beneath her ("I am better educated than you") and she does not love him, revealing more of her traits.
"No — no — I cannot. Don't press me any more — don't. I don't love you ...."
In Chapter 5, Bathsheba leaves the environs of Oak's home to go to her uncle in Weatherbury. Here begins Oaks long tragic suffering (a specialty of Hardy's realism). The son of Oak's sheep dog, George, was being trained to drive sheep. One night the son of George drives the sheep with good will and energy over a precipice. Oak is ruined. He sells what he has left. Thus begins his wanderings and his search for work.
A horrible conviction darted through Oak. With a sensation of bodily faintness he advanced: at one point the rails were broken through ... Oak looked over the precipice. The ewes lay dead and dying at its foot ...