There are many myths in many different cultures that have different stories regarding the constellations in the night sky. The main myths we hear today stem from Asian and European backgrounds.
Probably the most famous myth about Aquila, the constellation which encompasses Altair, involves Prometheus, a Titan god. Prometheus was a Titan gods who eventually became an adviser to Zeus. Prometheus was kind towards humans and seeing how they suffered because they had no fire, ended up stealing a ray from the Sun which he smuggled down to earth for humankind to use. Zeus did not believe that humans deserved the gift of fire, and was furious that Prometheus help them without his permission. Prometheus was consequently chained to the side of a mountain, stripped of his clothes, and was continually attacked by Aquila. Because Prometheus is a Titan god and therefore immortal, his wounds healed up every night only to be opened up again the next day by Aquila. After many years of this continued punishment, Prometheus was saved by Hercules who supported this kind deed Prometheus had done for mankind. Hercules then used his bow and arrow, shot and killed Aquila who was then placed by Zeus to soar to the heavens.
In India, Altair along with the two stars beside it, Beta and Gamma (Tarazed and Alshain), are said to be the celestial footprints of the god Vishnu.
Altair is separated from the similar-looking star Vega, in the constellation Lyra, by the starlit band of the Milky Way. In Asia, this hazy band across the sky is known as the Celestial River. One common story in China, Japan, and Korea, is that a young herdsman (Altair) falls in love with a celestial princess (Vega), who is in charge of weaving the fabrics of heaven. Vega fell so madly in love with the Altair that she neglects her duty of weaving the heavens. Vega’s father, the Celestial Emperor, declares that Altair must stay away from his daughter, on the opposite side of the Celestial River. The Emperor finally listens to the princess’s pleas and allows Altair to cross the Celestial River once per year, on the seventh day of the seventh month. In Japan, Altair is known as Hikoboshi, and Vega as Orihime (or Tanabata).