The first segment of Dragonflight was a Hugo award winning novella (called Weyr Search) prior to publication of the entire book.
Warning: Wikipedia contains spoilers
Dragonflight chronicles the story of Lessa, a daughter of the noble family of Ruatha Hold on the northern continent of Pern. She disguises herself as a drudge (higher than a slave, but lower than a servant) when the rest of her family is killed by the cruel and greedy Fax. F'lar, wingleader at Benden Weyr and rider of the bronze dragon Mnementh, finds Lessa while Searching for a rider for the Queen dragon that is about to hatch. After defeating Fax in single combat (following the rules of the Pernese code duello), F'lar convinces Lessa to give up her birthright as Lord Holder of Ruatha Hold and join him at Benden Weyr as a candidate for Weyr Lady. Lessa Impresses the Queen dragonet Ramoth and becomes the new co-leader of the last active Weyr. On Ramoth's first mating flight, she chooses Mnementh as her mate. By Weyr tradition, this makes F'lar the Weyrleader of Benden Weyr. Together, Lessa and F'lar warn a dangerously unprepared Pern for the upcoming Thread scourge. They revitalize the Weyr and start working closely with the Lord Holders and the Harpers to prevent the deadly rain of Thread from destroying the Pernese civilization.