Future Tense: Usage (Syntax)

Used just like in English to indicate that something will happen, will be done later on.
In English: I shall watch TV tonight. I'm going to work hard in future. I'm going to Greece next summer.
For morphology (forms taken by various types of verbs) see here.

Doesn't exist in English and is best translated, most of the time, as "about to [do, sing, work, sit down and rest....]".

The future infinitive endings are the same as regular -ω verb present infinitive endings:
active infinitive ends in unaccented -ειν
and middle ends in unaccented -εσθαι
Contract futures (see here) end in -εῖν, -εῖσθαι of course.

In Greek it is used

• in indirect speech (that will have to wait, a little too complicated just now)
  
• after μέλλω meaning "I'm about to":
  We've seen, chapter 5b, Ο ΑΡΓΟΣ ΤΑ ΜΗΛΑ (ΠΡΟΒΑΤΑ) ΣΩιΖΕΙ
  The wolf is about to attack.
  Instead of the present infinitives "ἐμπίπτειν, καθεύδειν, ποιεῖν, βοᾶν, κεντεῖν, the Greeks would generally have used the future infinitives:
  Change these 5 sentences using future infinitives.

Doesn't exist in English, corresponds to the Latin -urus form ("ave Caesar, morituri te salutant"):
Those travelling to Athens: οἱ Ἀθήναζε πορευόμενοι (present participle)
Those about to travel to Athens: οἱ Ἀθήναζε πορευσόμενοι