A distinction is made between Greek gardens, made in ancient Greece, and Hellenistic gardens, made under the influence of Greek culture in late classical times. Little is known about either.
Minoan gardens.
Before the coming of Proto-Greeks into the Aegean, Minoan culture represented gardens, in the form of subtly tamed wild-seeming landscapes, shown in frescoes, notably in a stylised floral sacred landscape with some Egyptianising features represented in fragments of a Middle Minoan fresco at Amnisos, northeast of Knossos. In the east wing of the palace at Phaistos, Maria Shaw believes, fissures and tool-trimmed holes may once have been planted. In the post-Minoan world, Mycenaean art concentrates on human interactions, where the natural world takes a lessened role, and following the collapse of Mycenaean palace-culture and the loss of the literacy connected with it, pleasure gardens are unlikely to have been a feature of the Greek Dark Age.
Literature.
In the eighth century BC, the works of Homer contain a reference to gardens, the Neverland of Alcinous, in the purely mythic Phaeacia, which stood as much apart from the known world of Homer's hearers as it did from the heroic world of Achaeans he was recreating, with much poetic license: "We live far off", said Nausicaa, "surrounded by the stormy sea, the outermost of men, and no other mortals have dealing with us."
Now, you'll find a splendid grove along the road— ;br ;
poplars, sacred to Pallas— ;br ;
a bubbling spring's inside and meadows run around it. ;br ;
There lies my father's estate, his blossoming orchard too, ;br ;
as far from town as a man's strong shout can carry. ;br ;
Take a seat there.
The gardens of the palace were possessed of an unearthly lushness, in the fenced orchard outside the courtyard, fronting the high gates:
Here luxuriant trees are always in their prime ;br ;
pomegranates and pears, and apples glowing red, ;br ;
succulent figs and olives swelling sleek and dark. ;br ;
And the yield of all these trees will never flag or die, ;br ;
neither in winter nor in summer, a harvest all year round.
The description is beloved of writers on gardens, nevertheless. 
Poetic descriptions of the Greek landscape and flora are well known from early times: the tale of Narcissus, Daphne's transformation into a laurel, oaks inhabited by dryads and streams with nymphs, and Persephone eating pomegranate seeds, but it is not until the Hellenistic era that gardeners write treatises on their work, called "kepourika".
No such gardens were known to Homer's contemporaries, as far as archaeologists can discern, any more than palaces like Alcinous', whose very doors were of bronze. The gardens of Greek myth were "untended" gardens, maintained in orderly fashion simply because order, "themis", was in the nature of things, as in the garden of the Hesperides, which was an orchard.
Classical Greece.
Archaeologists have not identified planted courtyards within the palaces of Mycenean culture nor in Greek houses of the Classical period. When the editors of a symposium on Roman gardens included a contribution on the expected Greek precursors, Brunilde Sismondo Ridgway's article prompted a reviewer to observe, "For all practical purposes there appear to have been no gardens of any sort in Greek city homes, beyond perhaps a few pots with plants." Aside from vegetable plots and orchards, Ridgway found some literary and a small amount of archaeological evidence for public, or semi-public gardens linked to sanctuaries. In fifth- and fourth-century Athens, some public places were planted with trees, as Plato directed in his "Laws", "The fountains of water, whether of rivers or springs, shall be ornamented with plantings and buildings for beauty", though he does not offer details.
In 1936, the surroundings of the Temple of Hephaestus at Athens were excavated to bare rock, in which rectangular planting pits were identified, which ran round three sides of the temple but not across its front and were lined up with the columns of the temple. In their bases were the shattered remains of flower pots in which layered stems had been rooted; however, associated coins show that the first of these plantings had been made not before the third century BC. By that time, in mainland Greece and Ionia, the influence of Achaemenid Persia was paramount in humanly-tended gardens, but in the previous century, of Alexander the Great, Plutarch observed that as a boy he would inquire of Persian visitors to his father's court in Macedon, about Persian roads and military organization, but never of the Hanging Gardens of Babylon; Herodotus, who probably visited Babylon in the mid-fifth century, does not mention the hanging gardens. Xenophon, under Achaemenid Persian influence, planted a grove upon his return to Athens. The myth, set in Macedon, of Silenus discovered drunken by Midas can be dated to the Hellenistic period simply from its setting, a rose garden.
In Athens, the first private pleasure gardens appear in literary sources in the fourth century. The Academy had its site in an ancient grove of plane trees sacred to an obscure archaic hero, Akademos. Sacred groves were never actively planted, but simply existed from time immemorial and were "recognized" as sacred: they have no place in the history of gardens, save as a resort for contemplation and, at Plato's Academy, for intellectual discourse. By contrast, the olive trees in the Academy, watered by the river Cephissus, were planted, grown, it was said, from slips taken of the sacred olive at the Erechtheum. The "temenos", or sacred ground, of the Academy was walled round, for ritual reasons, as pleasure gardens would be, for practical ones; within its precincts were buildings: small temples, shrines and tombs, in addition to that of the presiding hero. 
In 322 BC, Theophrastus, the father of botany, inherited Aristotle's garden, along with his scholars and his library; of the garden we know only that it had a walk, and that Theophrastus lectured there: it may have been in some respects a botanical garden with a scientific rather than recreational purpose. On his return to Athens in 306 BCE, the philosopher Epicurus founded The Garden, a school named for the garden he owned about halfway between the Stoa and the Academy that served as the school's meeting place; little is actually known of the ascetic philosopher's garden, though in cultural history it grew retrospectively in delight: of his garden at Geneva, "Les Délices", Voltaire could exclaim, with more enthusiasm than history, "It is the palace of a philosopher with the gardens of Epicurus—it is a delicious retreat". Gardens of Adonis, under Syrian influence, were simple plantings of herbal seedlings grown in saucers and pots, which, when they collapsed in the heat of summer, were the signal for mourning for Adonis among his female adherents: these were not gardens in any general sense.
Hellenistic gardens.
Though Harpalus, Alexander's successor at Babylon, grew some Greek plants in the royal palace and walks, mainland Greece, mother of democracy and Western cultural traditions, was not the mother of European gardens: the great Hellenistic garden was that of the Ptolemaic dynasty in Alexandria, a grand, walled paradise landscape that included the famous Library of Alexandria, part of the Musaeum. Water-powered automata and water organs featured in Hellenistic gardens, playthings devised by technicians such as Hero of Alexandria, who, not incidentally, also devised machinery for the stage. In late classical times the peristyle form became dominant in grand private houses. This was a paved courtyard, which came to be outfitted with potted plants, a Persian and Egyptian idea, surrounded by a roofed colonnade. It was used for palaces and gymnasia.
Roman decorative gardening first appeared after Roman encounters with gardening traditions of the Hellenized East.
References.
 ;templatestyles src="Reflist/styles.css" / ;