aufschreiben
to write down
To record something in writing so as not to forget it; to make a note.
Kannst du mir bitte deine Adresse aufschreiben?
Can you please write down your address for me?

to write down
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to write down
To record something in writing so as not to forget it; to make a note.
Kannst du mir bitte deine Adresse aufschreiben?
Can you please write down your address for me?

'Aufschreiben' (to write down) is a separable verb. The prefix 'auf-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ich schreibe mir deine Nummer sofort auf.
I'll write down your number right away.
'Aufschreiben' (to write down) is very often used with a dative object that indicates the person for whom something is written down. The structure is: jemandem (dative) etwas (accusative) aufschreiben.
Der Polizist schrieb dem Zeugen seine Kontaktdaten auf.
The police officer wrote down his contact details for the witness.
In the meaning 'notieren' (to note down), the verb is often combined with information you don't want to forget: write down an address, a phone number, a thought, an idea, or a shopping list.
Er hat sich während des Vortrags viele Notizen aufgeschrieben.
He wrote down a lot of notes during the lecture.
When the verb is used in the context of doctors, patients, or pharmacies, it means 'ein Rezept ausstellen' (to issue a prescription) or 'verordnen' (to prescribe). Signal words are 'Arzt' (doctor), 'Rezept' (prescription), or names of medications.
Meine Ärztin hat mir Antibiotika aufgeschrieben.
My doctor prescribed me antibiotics.
In a shop, bar, or restaurant, 'etwas aufschreiben lassen' (to have something put on a tab) means that you don't pay immediately, but have the amount put on a bill. You often hear the question: 'Können Sie das aufschreiben?' (Can you put that on my tab?).
Ich habe mein Portemonnaie vergessen, können Sie die Getränke bitte aufschreiben?
I forgot my wallet; can you please put the drinks on my tab?
to write
'schreiben' and 'aufschreiben' can both mean that you record words or information in writing. 'schreiben' is the general word and works for texts of any length, for example letters, messages, or assignments. 'aufschreiben' is used especially when you record something so that you do not forget it. It is often about notes, names, addresses, appointments, or ideas. Learners may confuse the words because both look very similar. The practical difference is: you write a text, but you write down an important piece of information.

Zur Vorbereitung schreibe ich mir bei der Arbeit alle Fragen auf.
To prepare, I write down all the questions at work.
In der Bibliothek schreiben wir morgen den Text für unser Referat.
Tomorrow in the library we are writing the text for our presentation.