~ませんか
Politely invite someone to do something
You’ll be able to invite someone to join you politely without sounding pushy.

コーヒーを飲みませんか。
koohii o nomimasen ka.
What do you think this sentence means?
Would you like to have some coffee?
Invite someone politely
Use ~ませんか to invite someone to do something together. The negative form makes the invitation softer than a direct command or request.
一緒に映画を見ませんか。
issho ni eiga o mimasen ka.
Would you like to watch a movie together?
Verb stem + ませんか
Use the polite negative question form as an invitation.
コーヒーを飲みませんか。
koohii o nomimasen ka.
Would you like to have coffee?
週末、出かけませんか。
shuumatsu, dekakemasen ka.
Would you like to go out this weekend?
一緒に勉強しませんか。
issho ni benkyou shimasen ka.
Would you like to study together?
~ましょうか vs ~ませんか
Both ask a question, but ませんか extends a fresh invitation and gives room to say no. ましょうか is used to decide the next immediate step together or offer help.
~ませんか, invitation
一緒に映画を見ませんか。
issho ni eiga o mimasen ka.
Would you like to watch a movie together?
A polite, pressure-free invitation to start a new plan.
~ましょうか, next step / suggestion
映画を見ましょうか。
eiga o mimashou ka.
Shall we watch a movie?
Proposes the next immediate step when already together.
明日、一緒に昼ご飯を食べませんか。
ashita, issho ni hirugohan o tabemasen ka.
Would you like to have lunch together tomorrow?
今晩、映画を見ませんか。
konban, eiga o mimasen ka.
Would you like to watch a movie tonight?
この店でコーヒーを飲みませんか。
kono mise de koohii o nomimasen ka.
Would you like to have coffee at this shop?
6 more examples in the grammar path — free for a limited time.