は、には、とは、では…の違いを教えてください

Question

Answer

This is a tough and interesting question.
I'll explain radically.

*** What is 'は'? (it does't indicate subject)

私はAKIです。(I am AKI)
私がAKIです。(I am AKI)
Two sentences look like same.but gramatical structures are completely different.

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*** 私がAKIです。(I am AKI)

Very roughly saying, the structure is like this:

私が（I as subject)
AKI (AKI as object)
です （am as verb)

OK, let's suppose '～が' is subject.

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*** 私はAKIです。(Me, it's AKI)

私は is not subject.

if you regard ～は as subject, you cannot explain the following sentences.

- 「象は鼻が長い」（The elephant has a long nose)
    which is subject, 象？ 鼻？

- What's your order? -> 「僕はコーヒー」
　　　（hey, you are a human, not coffee !)

- 「あいつは殺す」
　　this means, in 98% case, "I/We'll kill him"
    very rarely means "He kills"
            ※ if you say「あいつが殺す」, this 100% always means "He kills"

- 「男は度胸、女は愛嬌」
　　means: "it's important for men to have courage, for woman, loveliness.", but Men __is not__ courage. Men is creatures and courage is a state of mind.

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*** Then What is 'は'？

One of the functions of 'は' is 「提題」"to raise the theme/issue of the sentence/conversation".

Clumsily saying, it means "talking about"

- 「象は鼻が長い」
  -> Talking about the elephant, it has a long nose

- 「僕はコーヒー」
  -> Talking about me, it's coffee (I'll order a cup of  coffee)

- 「あいつは殺す」
  -> Talking about him, it's to kill (I/We will kill him)

- 「私はAKIです」
  -> Talking about me, it's AKI(My name is AKI)

+++ 応用（application)

「僕はコーヒー、あいつは紅茶」
　　　-> Talking about me, it's coffee. And him, it's tea.
「あいつは殺すが、お前は生かす」
　　　-> Talking about him, it's to kill. But you, it's to let live.
「私はAKIで、彼はKIM」
　　　-> Talking about me, it's AKI. And him, it's KIM

「男は度胸、女は愛嬌」
　　　-> Talking about men, it's courage, while women,loveliness.

(to be continued)