knüpfen
to tie
To make a knot in order to connect two or more threads, ropes, or ribbons.
Er knüpfte die Schnürsenkel seiner Wanderschuhe fest.
He tied the laces of his hiking boots tightly.

to tie / make
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to tie
To make a knot in order to connect two or more threads, ropes, or ribbons.
Er knüpfte die Schnürsenkel seiner Wanderschuhe fest.
He tied the laces of his hiking boots tightly.

You can recognize the exact meaning of 'knüpfen' (to tie/make) from the object. With 'Kontakten' (contacts), it is about social relationships; with 'Hoffnungen' (hopes), it is about a conceptual connection; and with 'Knoten' (knots) or 'Teppichen' (carpets), it is about the literal, manual activity.
Auf der Konferenz will ich neue Kontakte knüpfen.
At the conference, I want to make new contacts.
The expression 'Kontakte knüpfen' (to make contacts) is very common and means to build new social or professional relationships. Other typical objects in this sense are 'Beziehungen' (relationships), 'Freundschaften' (friendships), or 'ein Bündnis' (an alliance).
Im Ausland ist es anfangs oft schwer, neue Freundschaften zu knüpfen.
Abroad, it is often difficult at first to make new friendships.
When expectations, hopes, or conditions are connected with something, 'knüpfen' (to attach/connect) is used with the preposition 'an' and the accusative. The structure is: 'etwas an etwas (Akk) knüpfen' (to attach something to something [accusative]).
Das Unternehmen knüpft die Beförderung an die Bedingung, dass sie ein Projekt erfolgreich abschließt.
The company attaches the promotion to the condition that she successfully completes a project.
In its literal meaning, 'knüpfen' (to tie) is used for connecting threads, ropes, or ribbons by means of a knot. Typical objects are 'einen Knoten' (a knot), 'Schnürsenkel' (shoelaces), 'ein Band' (a ribbon), or 'ein Netz' (a net).
Kannst du mir helfen, eine Schleife in dieses Geschenkband zu knüpfen?
Can you help me tie a bow in this gift ribbon?
to connect / to bandage
'verbinden' and 'knüpfen' can both mean that a connection is created. 'verbinden' is the general word and works for many kinds of connections, for example technical, spatial, or mental ones. 'knüpfen' is more concrete when you make a knot, and it is also used in fixed expressions like 'Kontakte knüpfen' (to make contacts) or 'Hoffnungen an etwas knüpfen' (to attach hopes to something). Learners may confuse the words because 'knüpfen' often seems like a special type of 'verbinden'. In many everyday situations, 'verbinden' is more neutral; 'knüpfen' fits when it is really about knots or certain fixed phrases.

Auf der Messe hat Sofia viele neue Kontakte geknüpft.
At the trade fair, Sofia made many new contacts.
Dieses Kabel verbindet den Bildschirm mit dem Laptop.
This cable connects the screen to the laptop.