to pick up / to establish / to tie on
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to pick up on
To refer to something previous in order to continue or develop it further. This can refer to a conversation, an idea, or a tradition.
Ich möchte an die Diskussion von letzter Woche anknüpfen.
I would like to pick up on last week's discussion.
'Anknüpfen' is a separable verb. The prefix 'an-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er knüpft an die Erfolge des letzten Jahres an.
He is building on last year's successes.
The verb is based on 'knüpfen' (to tie a knot). The prefix 'an-' reinforces the idea of a connection. So you connect something to an idea, an object, or a person.
In seiner Rede knüpfte er an ein altes Zitat an.
In his speech, he picked up on an old quotation.
When referring to something that already exists or attaching something, 'anknüpfen' is used with the preposition 'an' and the accusative.
Die Präsentation knüpft an das Thema der Vorwoche an.
The presentation picks up on the topic from the previous week.
In this figurative meaning, you often refer to abstract things. Typical phrases are 'an eine Diskussion anknüpfen' (to pick up on a discussion), 'an eine Tradition anknüpfen' (to continue a tradition), or 'an eine Idee anknüpfen' (to build on an idea).
Mit diesem Projekt wollen wir an alte Erfolge anknüpfen.
With this project, we want to build on past successes.
The combination 'Kontakte anknüpfen' (to establish contacts) is a very common fixed expression. It means getting to know new people, usually in a professional or social context.
Im Auslandssemester konnte ich schnell neue Kontakte anknüpfen.
During my semester abroad, I was able to establish new contacts quickly.
to solve / loosen
'lösen' and 'anknüpfen' are clear opposites here. 'lösen' means to loosen or open something fixed, for example a knot. 'anknüpfen' means to attach something to something else with a knot. So these are two opposite actions: with 'lösen', a connection is opened; with 'anknüpfen', a connection is created.
Am neuen Rucksack knüpft Lisa ein kleines Namensschild an.
Lisa ties a small name tag onto the new backpack.
Vor dem Waschen löst Tom den Knoten in der Schnur.
Before washing it, Tom unties the knot in the string.