さえ is a 副助詞（ふくじょし） (adverbial particle) in Japanese that is used to place emphasis on something existing in certain state. It is often translated as ‘even’.
さえ has three primary meanings, which are as follows:
類推（るいすい） - Analogy, (A) is an outstanding example of something.
限定（げんてい） - Limit, (A) is all that is needed for something.
添加（てんか） - Addition, (A) compounds something that is pre-existing.
さえ is regularly paired with other particles and is often followed by verbs in negative form, with the overall meaning usually being determined by what part (B) of the sentence is conveying. Let’s look at a few examples.
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上級者（じょうきゅうしゃ）の彼（かれ）でさえ出来（でき）ないのに、あなたが出来（でき）るわけがないでしょう。
Even someone in the advanced class level can't do it, there is no way you can do it.
彼女（かのじょ）は親（おや）にさえ知（し）らせずに彼氏（かれし）と結婚（けっこん）をした。
She got married to her boyfriend, even without telling her parents.
彼（かれ）はストレスのせいで、晩飯（ばんめし）を食（た）べることさえ出来（でき）なくなった。
Due to him being stressed, he couldn't even eat.
タナカ君（くん）は酷（ひど）くない？彼女（かのじょ）を傷（きず）つけたのに、謝（あやま）りさえしなかったらしいよ。
Don't you think Tanaka-kun is a jerk? He hurt his girlfriend, but he didn't even apologize.
そんなの放（ほう）っておいてさえいたら、すぐ直（なお）るよ。
Even if you leave it as it is, it will get well quickly.
In each of these cases, we can see how
さえ is showing that (A) is an extreme example of something.
は, も, でも, and
さえ are all 副助詞（ふくじょし） (adverbial particles) that can be thought of as having a relationship toward, and away from what is ‘expected’ in any given situation. This relationship can be seen here:
(A) は - (A) is completely expected, there is nothing unusual.
(A) も - (A) will be included as part of what is expected, but can be unusual.
(A) でも - (A) may or may not be included as part of what is expected, and can be unusual.
(A)
さえ - (A) is separated completely from what is expected, and is unusual.
Due to this unexpected and unusual situation that
さえ always presents, it is regularly translated as ‘let alone (A)’, or ‘not to mention (A)’.
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このレベルはプロでさえ難（むずか）しいというのに、よくできたね。
I am impressed you were able to do this, let alone that it is difficult even for professionals.
トムがこんなに漢字（かんじ）を知（し）っているのは凄（すご）いと思（おも）うよ。日本人（にほんじん）でさえ漢字（かんじ）は難（むずか）しいのに。
Tom, I think it is impressive that you know this many kanji. Not to mention that it is difficult even for Japanese people.