Hystaspes (father of Darius I) different from Vishtaspa
Hystaspes (Old Persian: 𐎻𐏁𐎫𐎠𐎿𐎱 Vištāspa; Ancient Greek: Ὑστάσπης Hustáspēs) or Guštāsp (Persian: گشتاسپ Guštāsp) (fl. 550 BC), was a Persian satrap of Bactria and Persis. He was the father of Darius I, emperor of the Achaemenid Empire, and Artabanus, who was a trusted advisor to both his brother Darius as well as Darius's son and successor, Xerxes I.
The son of Arsames, Hystaspes was a member of the Persian royal house of the Achaemenids. He was satrap of Persis under Cambyses II, and probably under his second cousin Cyrus the Great also. He accompanied Cyrus on his expedition against the Massagetae. However, he was sent back to Persis to keep watch over his eldest son, Darius, whom Cyrus, after a dream, suspected of considering treason.
Besides Darius, Hystaspes had three sons: Artabanus, Artaphernes, and Artanes, as well as a daughter who married Darius' lance-bearer Gobryas.Ammianus Marcellinus makes him a chief of the Magians, and tells a story of his studying in India under the Brahmins, an event that would correspond to the Achaemenid conquest of the Indus Valley:
"Hystaspes, a very wise monarch, the father of Darius. Who while boldly penetrating into the remoter districts of upper India, came to a certain woody retreat, of which with its tranquil silence the Brahmans, men of sublime genius, were the possessors. From their teaching he learnt the principles of the motion of the world and of the stars, and the pure rites of sacrifice, as far as he could; and of what he learnt he infused some portion into the minds of the Magi, which they have handed down by tradition to later ages, each instructing his own children, and adding to it their own system of divination".
In ancient sources, Hystaspes is sometimes considered as identical with Vishtaspa (the Avestan name for Hystapes), an early patron of Zoroaster.The  name of Hystaspes occurs in the inscriptions at Persepolis and in the Behistun Inscription, where the full lineage of Darius the Great is given: