auxiliary verb
will; shall
Expresses the speaker's volition or intention. Attaches to the stem of non-五段 verbs (e.g., 食べる→食べよう).
I'll get up early tomorrow.
auxiliary verb
Used for suggestions or invitations, often with a sense of 'shall we?'. Attaches to non-五段 stems.
Let's watch a movie together.
auxiliary verb
Expresses speculation or uncertainty about something. Often used in self-directed questions or when thinking aloud.
I wonder if he has already gone home.
よう expresses the speaker's affirmative volition or conjecture ('will do/probably will'), the opposite of まい's negative volition or conjecture ('will not/probably not').
よう is the parallel volitional/conjecture auxiliary used with ichidan and irregular verbs (食べよう, しよう), while う is used with godan verbs (書こう) — learners must pick the right one based on conjugation class, not meaning.
Derived from the classical volitional auxiliary む (mu), which shifted to う (u) for 五段 verbs and よう (yō) for other verb classes. The exact phonological development is complex but well-established.