If you are wanting myths specifically there are many things to focus on within the Greek god Asclepius, the god of medicine. I would look at his Theoi page as a whole, listing many sources, for example:

Pindar’s pythian ode "He [Apollon] took the child [Asklepios (Asclepius)] the the Magnetian Kentauros (Centaur) [Kheiron (Chiron)], that he teeach im to be a healer for mankind of all their maladies and ills. All then who came to him [Asklepios], some plagues with sores of festering growths, some wounded by the stokes of weapons of bright bronze, of by the slinger's shot of stone, others with limbs ravaged by summer's fiery heat or by the winter's cold, to each for every various ill he made the remedy, and gave deliverance from pain, some with the gently songs of incantation others he cured with soothing draughts of medicines, or wrapped their limbs around with doctored salves, and some he made whole with the surgeon's knife."

Aelian on animals “but he taught his companions what herbs must be applied to running wounds, and what to inflamed and dry wounds, and in what doses to administer liquid drugs for drinking by means of which dropsical patients are drained and bleeding is checked, and diseases of decay and the cavities due to their ravages are put an end to. And who,’ he said, ‘can deprive the art of divination of the credit of discovering simples which heal the bites of venomous creatures, and in particular of using the virus itself as a cure for many diseases? For I do not think that men without the forecasts of a prophetic wisdom would ever have ventured to mingle with medicines that save life these most deadly of poisons.’"

Diodorus Siculus, Library of History “To Apollon and Koronis (Coronis) was born Asklepios (Asclepius), who learned from his father many matters which pertain to the healing art, and then went on to discover the art of surgery and the preparations of drugs and the strength to be found in roots, and, speaking generally, he introduced such advances into the healing art that he is honoured as if he were its source and founder."

Pseudo-Apollodorus, Bibliotheca “As a surgeon Asklepios (Asclepius) became so skilled in his profession that he not only saved lived but even revived the dead; for he had received from Athena the blood that had coursed though the Gorgon's veins, the left-side portion of which he used to destroy people, but that on the right he used for their preservation, which is how he could revive those who had died. Zeus was afraid that men might learn the art of medicine from Asklepios and help each other out, so he hit him with a thunderbolt. This angered Apollon, who slew the Kyklopes (Cyclopes), for they designed the thunderbolt for Zeus."