especially in everyday conversation, is 'mal'

it can stand alone

but (it) also appears in many different combinations

with other words

'first of all', 'already', 'just once', 'not even once', 'now', and so on

today, we'll take a closer look at what 'mal' means

 I'm not talking about the noun 'Mal' today

because the video would get too long

 the meaning of the noun isn't that complicated anyway

so, we're talking about the lowercase 'mal', which can be an adverb or a particle 

we encounter 'mal' very often in both functions in spoken language 

as an adverb, 'mal' is a shortened form of 'einmal' (once)

let's look at a simple example dialogue: - 'Do you know this book?'

'yes, I read it once'

here, 'mal' means 'sometime in the past'

 I don't remember exactly when I read the book

 or perhaps that's not important right now

in any case, it was a long time ago

I didn't read it yesterday, or last week, or even last month

 it was quite a while ago

if I phrase this sentence without 'sometime' ('mal'), and say, 'Yes, I read that'

I'm not giving any indication of when I read it           

I could theoretically have read it yesterday

furthermore, without 'sometime' ("mal") the sentence can sound ...

... the sentence can sound as if I know the book quite well

I've read it and could tell you a lot about it

with 'sometime', ('mal) I'm more like saying, 'Yes, I read the book at some point

but I don't remember it very well

I'm not completely familiar with it'

so, 'sometime' ('mal') has a somewhat weakening effect overall

the statement of the whole sentence becomes a bit weaker and less precise

interestingly, 'sometime' ('mal') can also refer to a point in the future

 I could say, 'Do you know this book?'

 'no, but I definitely want to read it sometime'

this means: I want to read this book sometime in the future

another example: 'I will go to the doctor about my headache sometime'

so, I will go to the doctor sometime

 I don't specify when. I remain vague here as well

 I don't commit to when I will do something  

another example: I haven't heard from my brother in a long time

I will call him sometime

this could mean that I call him right now

... or that I will call him next week or sometime

 if I were to say I will call him - without 'sometime' ('mal') - it would sound much more decisive

I will definitely call him