Why was Dorne never conquered by Aegon the Conquerer? Details explored 

Aegon the Conquerer was the first ruler of the infamous House of Targaryen, and the first to rule over the Seven Kingdoms in George R.R. Martin's fictional The Song of Ice and Fire novels.

Born to Lord Aerion Targaryen and Lady Valaena Velaryon, he is regarded as the first ruler of the Seven Kingdoms. The first Targaryen king conquered all of Westeros owing to a dream he had, popularly known as Aegon's prophecy.

The popular series House of the Dragon mentioned this prophecy, where Aegon the Conquerer foresaw "the end of the world of men." As per his prophecy, it was a Targaryen ruler who would sit on the iron throne and unite the seven kingdoms in a battle against an otherworldly evil.

Be it Aegon's ambitions or his prophetic dream, he set out to conquer all of Westeros. He even managed to achieve the same, except for one very important kingdom, Dorne, which could not be captured due to the Dornishmen's refusal to surrender and the tactics they employed in war, making full use of their desert and mountain terrains, thus complicating navigation and battle for the opposition.

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Dorne remained the only unconquered kingdom under Aegon the Conquerer's rule

Aegon the Conquerer reigned supreme with the use of dragons, unique to the house of Targaryen. He strengthened his rule over the seven kingdoms with the help of his sister-wives, Visenya and Rhaenys.

As per George R.R. Martin's books, the seven kingdoms consisted of the areas divided as the North, the Vale, the Iron Islands, the Riverlands, the Westerlands, the Stormlands, and the Reach.

While Aegon the Conquerer managed to bring all of Westeros under his rule, Dorne (ruled by the House of Tyrell) remained the only place he was unable to conquer. Aegon first decided to use diplomacy to subjugate Dorne to the Iron Throne. However, after a year of talks with no results, he decided to use force to conquer Dorne.

The Targaryens and the Tyrells engaged in what is termed as the first Dornish War in The Song of Ice and Fire. Queen Rhaenys Targaryen led an army into Dorne, but the Dornish would not surrender. They concealed and vanished into their mountains and deserts.

In the First Dornish War, the Targaryens faced opposition from the Dornishmen after Aegon's conquest of the other Westerosian kingdoms. Both suffered greatly during the conflict, yet the Dornishmen did not back down. The Red Mountains in the west provided a route for Targaryen ground armies to invade Dorne, but they were routed via the small valleys and chokepoints.

The war led to the death of Queen Rhaenys, who fell after her dragon, Meraxes, was wounded in battle. The Dornish resistance to the Targaryen conquest is attributed to their war tactics. They understood that a battle against the dragons would be futile, thus they used guerilla warfare by retreating into the desert and mountains and launching surprise attacks.

Aegon the Conquerer could never conquer Dorne, where the desert and mountain terrain, coupled with the harsh Dornish weather, made it too tricky even for a battle with the dragons on his side.

When Princess Meria Tyrell passed away from old age, the conflict came to an end. Her son Prince Nymor took over as ruler, offering the Targaryens peace on equal terms while maintaining Dorne's independence. Aegon acceded to his requests and let Dorne remain a free kingdom. Aegon the Conquerer maintained cordial relations with the kingdom of Dorne till his death.