In my opinion, the correct English translation would be "He is writing me a book".
Unlike many other languages, the present simple and present continuous in English are not used interchangeably. The present simple requires a time frame over multiple instances of time (I work on weekdays, I go shopping at the weekend, I usually babysit in the evening) whereas the present continuous describes an activity you are doing in one instance of time either right now or in the future: I'm working (can only mean right now), I'm going shopping this weekend (you can only exist in one weekend at a time), I'm babysitting this evening (you can't babysit on every evening that exists in your life all at once hence why 'I babysit this evening' would be wrong).
But not all versions of English choose to differentiate between these concepts for example, in Indian English, it is perfectly correct to say "I'm working on Mondays". British English (and others) has its own issues with grammar for example, our rules don't allow us to actually invite people to do things.
We can't say "I invite you to my house tonight" to someone because as I mentioned, we can't use the present simple to talk about an action we are currently doing so you'd think that we would say "I'm inviting you to my house tonight" but we also can't say that because the present continuous implies that the action will still 'continue' at least once you have finished speaking! Also, it would sound like you were talking about yourself in the third person so we just don't.
What we end up doing is just hypothetically inviting people: we say "I would like to invite you to my house tonight" and then the other person says "Oh, that would be nice" and then both parties just pretend that the invitation took place. Then of course, we have that running joke in England (which never gets old) where the inviter finally replies: "Well, too bad because you're not invited!" - haha - it's the same with 'offer'. We don't ever offer people things. We just ask questions. The most common way to invite or offer is to ask a question: "Would you like a cup of tea?", "Yes, please. Two sugars, a bit of skimmed milk but not from the vending machine, from the milk in the fridge", "Ok, well the canteen is just down the hall".
Never. gets. old.
So, in short:
Duo's answer here is incomplete as it requires a time frame over multiple instances of time. Duo should get this clear because some people use the present simple and present continuous interchangeably in their own language and they need to learn that we don't do that in English.
I believe that "He writes me a book." is grammatically correct, although it is not likely that a native English speaker would use this construction without adding a "time phrase" at the end of the sentence. For example: "He writes me a book every year." We can use the present simple tense to make a general statement about an action without a time phrase: "He writes books".
I agree that "He is writing me a book" is the construction that a native speaker would more likely use for this translation. This is the present continuous tense and implies that this action is happening right now. In my opinion, both tenses can be used.
A native English speaker would have to add a (multiple) time frame because you can't use the simple present tense to talk about something you are doing now. The simple present is used for general time frames like "On Mondays, I write books". "He writes me a book whenever I ask him to". I think Latin language speakers (definitely Spanish) use the present simple for current actions: "I go to the shop" when they mean "I'm going to the shop" (i.e. right now) but it's grammatically incorrect. You can only use the present simple with a 'multiple' time frame.
"He writes books" works because 'books' is in the plural so the sentence is talking about books being written over multiple instances of time. The present simple (He writes) needs a multiple time frame. The present continuous (He's writing) needs a singular time frame although when we don't add one, it is assumed that we mean 'right now'.
I'm reading a book -- 'right now' is implied. I read him a book -- when? (assume 'read' is in the present) - all the 'bits' of a sentence are there (subject, verb, object etc.) and the words are in the correct order but the sentence/idea is incomplete.
To expand: You can't exist in more than one place/moment of space and time so in English we separate things you do on multiple days (Mondays, weekdays, weekends) from things you are doing in one instance of time (today, Monday, this week, tonight). "He writes me a book" is an incomplete sentence and if someone said that to me, I'd ask "when?"
Because "Buch" is neuter and in accusative case for neuter indefinite pronoun is "ein". http://www.canoo.net/inflection/ein:Art:Indef:SG . examples:
- masculine noun (der Brief = the letter): Er schreibt mir einen Brief.
- feminine noun (die Notiz = the note): Er schreibt mir eine Notiz.
The stem is "ein" and we have to remember which ending we need to add according to case and gender.