ないで

～ないで (Without)
Verb ない form＋で

This is another kind of negative て form, that can only be used with verbs. This pattern treats ない as a な adjective/noun representing a state.
The で here transforms the verb and everything attached to it into the state of “not doing/having done something.” More simply, it means “without“.

Examples

• 人と話さないで生きる – Without talking to people, live. (live in a state of not talking to people).
• かさを持たないで出かけた。- He went out without an umbrella (Went out in state of not having an umbrella).
• 本を読まないでレポートを書いた – He wrote a report without reading the book.
  
  

ないでください

Please Don’t
Verbないで + ください

This verb form is also how we get the Negative ください form. Literally it means “without please”

• 見ないでください – Please don’t look. 
• しないでください – Please don’t do.

Like てください, the ください is commonly dropped in informal speech.

• 行かないで – Don’t go
• 死なないで – Don’t die. 
  
  

Comparison to なくて

This is sometimes confused with なくて, so here are a few comparison examples

• かさを持たなくて出かけた – Didn’t have umbrella so went out. ✖
• 傘を待たないで出かけた – Went out without an umbrella.〇
• 勉強しないで不合格だった – Failed without studying. — grammatically ok but weird△
• 勉強しなくて不合格だった – Failed since (they) didn’t study.〇
• 勉強しないで合格した。 – Passed without studying. 〇
  
  

なくて review chart

• Source 1 (Japanese)
• Source 2 (Japanese)
• Source 3 (English)