Argthtjtr

I am writing a presentation which should include an outline.

I would like to present a short background for my subject. However, I just wonder how to express my outline in correct English writing.

• Brief background on the subject.

or

• Brief background to the subject.

Which one is correct and why?

TO: Yes

Quoting se16teddy from https://forum.wordreference.com/threads/background-of-to.1171743/ :

in the expression "background to Y", Y is in the foreground.
e.g.:
The background to the story is the civil war.
Here, civil war is the background, story is foreground.
In your context, presentation is foreground, what you are going to say is background (right?). Therefore, YES.

ON: Yes

According to Cambridge Dictionary's entry on "background"

Background:
the conditions that existed before a particular event happened, and that help to explain why it happened:

Example:

Can you give me some background on (= information about the conditions that existed before) the situation?

I agree with the other answer, in that both are grammatical and you can find example uses of both phrasings.

• For some background on the Russian-Kazakhstani relationship, see "Russian Rumblings," in The Economist
  


• The aim of this book is to describe one possible formal background to mathematics

However, I’d like to provide a third option: no prepositional phrase at all.

I assume the audience will already know your topic. If your subject is the Ornithology of House Wrens, for example, why bother saying:

• Brief background on the ornithology of house wrens

when you can simply say instead:

• Background

and everyone will know what you are talking about?

This is especially true if your outline is destined for an overview slide. Why clutter up the slide with unneeded words?

As a footnote, when we first glance at the ngram, it looks like both prepositions are used, although on is more popular. However if you sift through the results, you’ll find that many of the hits are using the words on, to, and background in a very different way. For example:

• Gamma-Radiation Background on Board Russian Orbital Stations


• a blue background on panchromatic film without a filter


• to create a background on your Web page

Also:

• the patient's personal and family background to the consultant


• officers lacked the knowledge and background to evaluate applications fairly

So, in this case, the ngram doesn’t reliably show anything.