sich melden
to get in touch
To contact someone, for example by phone call or message.
Melde dich doch mal wieder, wenn du Zeit hast.
Do get in touch again sometime when you have time.

to report / get in touch
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to get in touch
To contact someone, for example by phone call or message.
Melde dich doch mal wieder, wenn du Zeit hast.
Do get in touch again sometime when you have time.

Most meanings of 'melden' are reflexive ('sich melden'), with the person carrying out the action themselves. The non-reflexive form 'etwas melden' (to report something) always means to pass information on to someone else.
Er meldet sich nie bei mir.
He never gets in touch with me.
The verb 'melden' is often used with prepositions. 'Sich bei jemandem melden' (to get in touch with someone) and 'sich für etwas melden' (to volunteer for something) are common. When you report something, you say 'etwas bei einer Stelle melden' (to report something to an office/authority).
Bitte melde dich bei deiner Ankunft am Empfang.
Please report to reception when you arrive.
When reporting information, you often use both a dative and an accusative complement: You report 'jemandem (Dativ)' (to someone, dative) 'etwas (Akkusativ)' (something, accusative). The accusative object is the information; the dative object is the person or office that receives it.
Der Zeuge meldete dem Polizisten seine Beobachtung.
The witness reported his observation to the police officer.
The phrase 'sich melden' is often used in connection with authorities, e.g. at the 'Einwohnermeldeamt' (residents' registration office) or 'Arbeitsamt' (employment office). It means to appear there in person in order to register.
Alle neuen Studierenden müssen sich bis Freitag im Sekretariat melden.
All new students must report to the office by Friday.
The meaning 'to raise one's hand' is typical in class or in meetings. If someone has a question or wants to say something, he or she must first 'sich melden' (raise their hand).
Der Lehrer fragt, wer die Antwort weiß, und drei Schüler melden sich.
The teacher asks who knows the answer, and three students raise their hands.
to report
'berichten' and 'melden' can both mean that information is passed on. 'berichten' is used when someone tells about an event, an experience, or a situation, often in somewhat more detail. Journalists also 'berichten über Nachrichten' (report on news). 'melden' is more concise and often more official: for example, you 'meldet' an accident, an error, or a piece of information to the responsible office or person. 'sich melden' also has other meanings, such as getting in touch, raising your hand in school, or volunteering for a task. The words can be confused because both have to do with information. As a guide: 'berichten' tells more; 'melden' passes on information in a targeted or official way.

Wir melden den Schaden sofort der Versicherung.
We report the damage to the insurance company immediately.
Die Verkäuferin berichtete nach dem Gespräch ausführlich von dem Problem mit dem Kunden.
After the conversation, the sales assistant gave a detailed account of the problem with the customer.