The Gerund (-οντας / -ώντας)
The GERUND (γερούνδιο) is Greek’s “-ing” form for a background action - English “while doing / by doing”. It is built from the PRESENT (imperfective) stem, and the ending depends on the verb group. GROUP 1 (stem-stressed) adds -οντας, and the stress STAYS on the stem - the ending NEVER takes a tonos: γράφω → γράφοντας, τρέχω → τρέχοντας, διαβάζω → διαβάζοντας. GROUP 2 (contracted) adds -ώντας, and the ώ ALWAYS carries the tonos: αγαπώ → αγαπώντας, μιλάω → μιλώντας, ρωτάω → ρωτώντας. A few high-frequency verbs build it on an extended present stem: τρώω → τρώγοντας, λέω → λέγοντας. The gerund is INVARIANT - one single form per verb, it never changes for person, number, or tense. The tonos rule is the whole game: -οντας bare, -ώντας stressed.
The rule
The gerund (γερούνδιο) is Greek's single “-ing” form for a background action - English “while doing / by doing”. It is invariable: one form per verb, built from the present (imperfective) stem, that never changes for person, number, or tense. The ending is set by the verb group, and the whole rule is the accent. Group 1 (stem-stressed) adds -οντας with the stress staying on the stem and no tonos on the ending: γράφω → γράφοντας, τρέχω → τρέχοντας, διαβάζω → διαβάζοντας (a few build on an extended stem - τρώω → τρώγοντας, λέω → λέγοντας). Group 2 (contracted) adds -ώντας with the ώ always stressed: αγαπώ → αγαπώντας, μιλάω → μιλώντας, ρωτάω → ρωτώντας. It does two jobs: simultaneous action (Περπατώντας στον δρόμο, είδα… “Walking down the street, I saw…”) and manner/means (Μαθαίνει διαβάζοντας “He learns by reading”). Its subject is always the main verb's, so use it only when one doer performs both actions - different subjects need a full clause (ενώ / όταν).