One might say "stories" about the Argonauts, rather than a singular story because many of the heroes involved in the famous quest shine in their own little adventures along the way. Hercules lost his lover. Orpheus made mythological history with his music. The female Atalanta joined the otherwise all-male crew and it took another woman to figure out how to achieve the quest's aim. Other heroes, like the twins Castor and Pollux, performed feats of brawn and derring-do, and the boat was magical:
The story of the Argonauts and their quest for the Golden Fleece is, like the story of the Caledonian Boar Hunt one a pivotal myth in Greek mythology and legend.
And straightway on a sudden there called to them in the midst of their course, speaking with a human voice, the beam of the hollow ship, which Athena had set in the centre of the stem, made of Dodonian oak. And deadly fear seized them as they heard the voice that told of the grievous wrath of Zeus. For it proclaimed that they should not escape the paths of an endless sea nor grievous tempests, unless Circe should purge away the guilt of the ruthless murder of Apsyrtus; and it bade Polydeuces and Castor pray to the immortal gods first to grant a path through the Ausonian sea where they should find Circe, daughter of Perse and Helios.
Apollonius Rhodius Book IV
Jason was the leader of the Argonauts and the person who had been sent off to acquire the Golden Fleece in order to claim his rightful slot as ruler or die in the effort. Along the way, he acquired the support and infatuation of a witch named Medea with whom he lived in apparent wedlock for many years.
Modern Retellings of the Story of the Golden FleeceThe Golden Fleece.
Lists of the ArgonautsThere are two main lists of the Argonauts here. One comes from Apollonius of Rhodes, and the other from the Library of a man identified as Apollodorus. Apollonius (fl. 3rd century B.C.) wrote the entire story of the quest for the Golden Fleece in a book called The Argonautica. Apollodorus or Pseudo-Apollodorus, since it was probably written by someone who lived later, is thought to have lived in the century after Apollonius. The Apollodoran account of the Golden Fleece and Medea appears at the end of the first book of his Library, chapters 9.16 to the end (I.9.28).
Hercules sets out with the Argonauts, but then, when some of the heroes stop off in the land of the Mysoi, his love interest, Hylas, goes missing. Hercules, unnoticed as missing by the Argonauts, stays behind to hunt, in vain.
Courtesy of Wikipedia
Orpheus helps the Argonauts in performing proper rituals to Apollo and also permits the Argonauts to cross the water where the Sirens lie in wait.
After sailing safely away from Colchis, Medea and Jason have cause to leave Jason's homeland and wind up in Corinth where they live together as man and wife, bringing up two children, but then Jason decides to marry the king's properly Greek daughter. Jason accuses Medea of bringing punishment upon herself because she is too possessive and jealous. Well, it would have been hard for Medea not to be, after having given up everything for the man in her life, but her response to her intolerable situation is even more horrible.
Medea was a grand-daughter of the Sun, Helios and something of a sorceress who worked magic with the aid of Hecate. Medea fell passionately in love with the young hero Jason who came to steal her father's fleece, and so she helped him -- treacherously. After their forced flight, she continued to commit frightening acts, and later, after Jason was completely through with her, she tried to make Theseus' father kill his only son.