Volitional form
let's (casual), I'll
Godan: o-row + う (行こう) · Ichidan: よう (食べよう) · しよう · 来よう
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The volitional form is the casual "let's": 行こう, "let's go"; 食べよう, "let's eat". It's what ましょう is to the polite register.
- godan verbs move the last kana to the o-row and add う: 行く → 行こう, 飲む → 飲もう, 帰る → 帰ろう
- ichidan verbs swap る for よう: 食べる → 食べよう, 見る → 見よう
- する → しよう, 来る → 来よう (こよう)
Said to yourself, it's a decision: よし、頑張ろう, "right, let's do this". With か, it's "shall we?" or, with かな, thinking aloud: 何を食べようかな, "hmm, what shall I eat?"
It's also the base of 〜ようと思う ("I'm thinking of doing"), the next point.
Register: Casual. The polite version is ましょう.
Examples
一緒に帰ろう。
Let's go home together.
明日、映画を見ようよ。
Let's see a film tomorrow.
疲れたね。ちょっと休もうか。
You look tired. Shall we take a break?
よし、今日から毎日走ろう。
Right, from today I'm going to run every day.
何を食べようかな。
Hmm, what shall I eat?