verbinden
to connect
To physically or technically link or join two or more things together.
Der Elektriker muss die beiden Kabel korrekt miteinander verbinden.
The electrician has to connect the two cables correctly.

to connect / to bandage
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to connect
To physically or technically link or join two or more things together.
Der Elektriker muss die beiden Kabel korrekt miteinander verbinden.
The electrician has to connect the two cables correctly.

'Verbinden' (to connect / to bandage) is an inseparable verb. The prefix 'ver-' remains firmly attached to the verb stem 'binden' (to bind) in all tenses and sentence positions.
Ich verbinde mein Handy mit dem WLAN.
I connect my phone to the Wi-Fi.
The verb 'verbinden' (to connect / to bandage) is the basis for important nouns like 'die Verbindung' (connection) and 'der Verband' (bandage; association). The different meanings of the verb are reflected in these nouns.
Die Verbindung zum Server ist fehlgeschlagen.
The connection to the server failed.
In many meanings (physical, telephone-related, mental), 'verbinden' (to connect) follows the pattern 'etwas/jemanden mit etwas/jemandem verbinden' (to connect something/someone with something/someone). The preposition 'mit' (with) is crucial here.
Diese Brücke verbindet die Insel mit dem Festland.
This bridge connects the island with the mainland.
In a telephone context, the question 'Können Sie mich bitte mit [Person/Abteilung] verbinden?' (Could you please connect me to [person/department]?) is a very polite and common phrasing to ask to be transferred.
Einen Moment, ich verbinde Sie mit der zuständigen Kollegin.
One moment, I will connect you to the colleague responsible.
In a medical context, 'verbinden' (to bandage) means treating a wound with a bandage. The object of the sentence is the wound or the injured body part.
Die Krankenschwester hat ihm die Wunde professionell verbunden.
The nurse bandaged his wound professionally.
The reflexive form 'sich verbinden' (to unite / to join together) means that people or groups join together to form a coalition or alliance. It emphasizes the shared action.
Die beiden Firmen haben sich verbunden, um ein neues Produkt zu entwickeln.
The two companies united to develop a new product.
to produce / establish
'verbinden' and 'herstellen' can both be used when a connection is made. 'verbinden' emphasizes that two things or people are linked with each other, for example cables, devices, or a phone call. 'herstellen' emphasizes more that something is created or made possible, for example a connection, a contact, or a state. So you can 'eine Verbindung herstellen' (establish a connection) and thereby 'zwei Geräte verbinden' (connect two devices). The words can be confused especially in technology and phone contexts. In practical terms: 'verbinden' is more about asking 'What is being linked with what?', while 'herstellen' is more about asking 'What is being brought about?'

Am Montag verbindet der Techniker den Drucker mit dem neuen Netzwerk.
On Monday, the technician connects the printer to the new network.
Nach dem Neustart stellt das Handy wieder eine Verbindung zum WLAN her.
After the restart, the phone establishes a connection to the Wi-Fi again.