This is a big subject! Hence the Roman numeral in the title. I expect to write more than one post on this.
First, the basics, then one specific situation. Ancient Greeks didn't cut, cleave, measure, and abuse time the way we do (see Michael Ende's Momo for a story about this-- beautiful!), mostly because the Greeks lived before the Industrial Revolution, when suddenly a nasty word called productivity became important.
Time had some importance to the Greeks, but they had no overall deity of time. Time, for them, wasn't as much of a thing as it is for us. They lived their lives, were grateful for the time they had, but didn't build it up into something more important than life.
On to a specific example about time:
The Horai (Horae in Latin, rhymes with "your eye") are a group of goddesses called The Hours or The Seasons. Lazy mythology teachers (or those who are pressed for time) tell their students that the Horai are the goddesses of the seasons (as in Fall, Winter, Spring, Summer). But they are a little more complex than that, and a little complexity can make all the difference.
Hora means, in Greek, a space of time. We get our word "hour" from it. But hora was not sixty minutes; it was a space of time with a beginning and an end. For the Greeks, it often meant a nice time, a period of time when good things were happening. Thus:
The poet Hesiod could name the Horai Eunomia (Good Government), Dike (Justice), and Eirene (Peace). Here he refers to those pleasant periods of time when things are going well in a state. And he would be the first to tell you that all three of these qualities do have a beginning and an end, because in between you find a lot of injustice, bad government, and war.
In the Iliad (Book 5, line 749), the Horai (as "hours" of the day) were cloud-gatekeepers:
Hera quickly flicked the horses with the lash,
And the automatic gates of heaven
Groaned open, as willed by the Hours,
Who control access to Olympus and heaven,
Opening and shutting the dense cloudbanks.
as always, Lombardo
Ever seen rays of sunshine beaming down between openings in the clouds? Homer probably figured the Horai responsible.
The Horai were also popular as attendants of Aphrodite. In this capacity they were often hard to tell apart from the Charites or Graces, goddesses who helped Aphrodite look even more beautiful than she was. We might think of the Horai here as periods of time which make you look good to your beloved-- like youth, or moonlit evenings, or that too-short golden time when your haircut has grown out just enough but not too much.
Consider the Horai also as seasons, in terms of pleasant parts of the year-- but not strictly as the four seasons, because there are not always four of them in the group, and the Greeks never thought of their year with four strict seasons.
Besides spring, summer, fall, winter, think of specific times during those seasons, such as when the first blossoms come up after winter rains (February-March); warm evenings after the grape harvest (October); the sunny days of summer that make pomegranates fat (August); a cold day when you see snow on the mountain for the first time (December, see photo above taken in Assisi, Italy).
What are your Horai-- your pleasant periods of life? These are like beneficent deities who make life easier for us.