Concern in this case means to focus on or concentrate on something. Actually this is the original meaning, and when it is personal it becomes more like worry. You can use the verb with the company to explain it's primary area of interest. So the main concern of the mayor may be to manage the city affairs. The ministry of defence is concerned with the army and navy. Tesla is concerned with both making cars and helping the environment. "Concerned about" expresses worry. "Concerned with" expresses concentration or focus.

"Concern" does -normally- mean worry, but in formal speech it's sometimes used to mean 'associated with'. Although it's a little bit hard to use it that way as there are only certain sentences it makes sense in. To give an example: "I read a book about Roman history." and "I read a book concerning Roman history." Mean the same thing. Although I'm not sure if my second sentence actually makes sense... but just as an example, that's how it would be used. Concerned about = Worried about. Concerned with = Regarding, about, associated with, etc. Edit: Whoops! Sorry, forgot to answer your other questions! 2. Erm, not really. It's a little hard to explain why because 'concerned with' isn't really used that often. Someone else might be able to explain better than I can. 3. Do you mean in the sentence about trigonometry or the one about your business? "Geometry is a branch of mathematics about lines, angles, curves and shapes" Makes sense, but "Our company about internet business..." Doesn't really make sense, as 'about' in this context is normally used when describing the subject piece of media (so a story, song, book, etc). A way you could start a sentence instead could be: "Our company, which takes part in internet business..."

1. in this case "concerned with" means "focused on", or "about" 2. No, in the example you gave, that makes your company sound like they are worried about the internet business. 3. "Concerned about" would probably get the meaning across to the reader, but it's more ambiguous. Hope that helps.