Examples have audio.

ke (“که”)

The word “که” is a particularly useful word in Persian. The main thing to learn is that it means “that” and “so that”. In reality, however, this word covers a broad area of meanings:

1-

We are already familiar with the word “که” meaning “that”. The noun preceding “که” (or any adjective following it, as in the second example below) gets a “ی” at the end. The “ی” can hardly be considered an indefinite article in this case.
ایمیلی که فرستادی خالی بود.
کیفِ بزرگی که خریدی گم شد.
The email that you sent was empty.
The big bag you bought was lost.
In the first sentence, the relative clause (the part starting with “که”) tells us which email the sentence is talking about. In the second sentence, the relative clause tells us which big bag is being talked about.
There are cases, however, where we want to explain something about the noun phrase, but the noun phrase itself is already known (definite). In such cases, we are not introducing it, but just giving some additional information about it (the technical term is a "non-restrictive relative clause"). The use of the suffix “ی” is prohibited in such cases. In English, we usually use "which" instead of "that" in such cases (if it's non-human, of course).
هیتلر که منظور چرچیل را می‌دانست،
قبول نکرد.
Hitler, who knew Churchill’s intention,
didn’t accept [it].

2-

We also learned that the word “که” can mean “who”. This particular form of the word “که” is pronounced as “کی” in Colloquial Persian.
با که حرف می‌زنی؟
Who are you talking to?

3-

Sometimes, we want to say that an incident happened right after another incident or as an aftermath of it. The easier-to-learn way of saying this is through one of the following structures:
وقتی تانک‌ها را دیدم، ترسیدم.
وقتی که تانک‌ها را دیدم، ترسیدم.
When I saw the tanks, I panicked.
This, however, is not the most common way of saying this, especially in spoken language. Usually, the word “که” alone is employed to mean “when”.
تانک‌ها را که دیدم، ترسیدم.
When I saw the tanks, I panicked.
This might look strange, especially because of the position of “که” in the sentence. As a rule of thumb, we may say that this type of “که” follows the first phrase of the sentence. Here are some examples:
زهرا که آمد، با او حرف بزن.
شب که بشود، صبا خودش می‌ترسد و
بر می‌گردد.
آماده که شدی، بگو.
برف که می‌آید، شهر سفید می‌شود.
حسین که کارش را تمام کرد، رفتند.
حسین کارش را که تمام کرد، رفت.
پیر که بشوید، می‌فهمید.
به مشهد که رسیدی، به من زنگ بزن.
باران که بیاید همه عاشق هستند.*
Talk to Zahra when she came.
When the night falls down, Saba will be scared and
will come back herself.
Say [it] when you became ready.
The city becomes white when it snows.
They left as soon as Hossein finished his job.
Hossein left as soon as he finished his job.
You [plu.] will understand when you become old.
Call me when you got to Mashhad.
When it rains, everyone is in love.

4-

Relatedly, “که” can appear between two separate sentences to mean "when".
نزدیکِ ظهر بود که اوّلین بمب را انداختند.
داشتم به تو فکر می‌کردم که زنگ زدی.
هنوز آتش انقلاب خاموش نشده بود که جنگ
شروع شد.
It was near noon when they dropped the first bomb.
I was thinking of you when you called.
The fire of the revolution was still burning
(lit.had not been extinguished) when the war started.

5-

The word “که” can appear after a noun phrase to imply that the truth of the sentence is guaranteed only for that particular noun phrase.
پول که ندارم، ولی طلا اگر بخواهی
دارم.
حسن که مریض است، ولی علی می‌تواند کمک کند.
محمد که از نمره‌ها راضی است.
خودت را که نمی‌توانی گول بزنی!
I don’t have money, but I do have gold
if you want.
Hassan is sick, but Ali can help.
(At least) Mohammad is happy with the marks.
You can’t fool yourself! (even if you fool others)

6-

The word “که” can be used to express surprise. Nothing particular about the noun phrase preceding it is conveyed in this usage. In fact, “که” in this usage can sometimes even come at the end of the sentence, after the verb itself.
باز که آمدی!
هنوز این‌جایی که!
این که کار نمی‌کند!
سلام، تو که گفته بودی نمی‌آیی!
You came again! (you weren’t supposed to come.)
You are still here! (You aren’t supposed to be.)
[but] this doesn’t work! (It was supposed to work.)
Hi, [but] you had said you won’t come!

7-

Strangely enough, “که” also suggest the obviousness of a sentence. Note that at least some of these have different intonational patterns. (Admittedly, the classification I'm offering here for the different functions of this word is not a very neat one. Like many things in the world of semantics, an accurate account of what this word does requires serious research, and the result will not be easy to present to the average language learner anyway).
تفنگ که داری؟
سیگار که نمی‌کشی؟
این که معلوم است!
من که گفتم تشنه‌ام! چرا آب نیاوردی؟
 
فقط گفتم نمی‌توانم. دروغ نگفتم که!
You do have a gun, don’t you?
You don’t smoke cigarettes, do you?
[but] this is obvious!
[but] I told you I’m thirsty! Why didn’t you bring
[some] water?
I only said I couldn’t (lit. can’t). I didn’t lie!

8-

The word “که” used between two sentences can mean “that”.
فهمیدم که هیچ‌کس خبر ندارد.
می‌دانم که می‌آیی.
I found out that nobody is informed.
I know that you will come.

9-

It can also come in this way as a synonym of “تا”, to mean “so that”.
بلند حرف می‌زنم که پدربزرگ هم بشنود.
امیر درس می‌خواند که بتواند از ایران برود.
I talk loudly so that grandfather hears [me] as well.
Amir studies so that he can leave Iran.
*Part of a poem by Iraj Zebardast