zusammenziehen
to move in together
To move into a shared apartment or house with one or more people.
Nach zwei Jahren Beziehung haben sie beschlossen, zusammenzuziehen.
After two years of being in a relationship, they decided to move in together.

to move in together / contract
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to move in together
To move into a shared apartment or house with one or more people.
Nach zwei Jahren Beziehung haben sie beschlossen, zusammenzuziehen.
After two years of being in a relationship, they decided to move in together.

'Zusammenziehen' (to move in together / to contract) is a separable verb. In a main clause, the prefix 'zusammen' goes at the end of the sentence. In a subordinate clause or an infinitive with 'zu', it remains attached to the verb.
Meine Freundin und ich ziehen nächsten Monat zusammen.
My girlfriend and I are moving in together next month.
The word consists of 'zusammen' (together) and 'ziehen' (to pull, to move). The basic idea of bringing things or people together in one place connects all the meanings of the word.
Der Magier zog die Enden des Tuchs zusammen und ließ die Münze verschwinden.
The magician drew the ends of the cloth together and made the coin disappear.
The grammar helps distinguish the meanings. The reflexive form 'sich zusammenziehen' describes a contraction or a storm gathering. The non-reflexive form without an object usually means moving into a shared apartment.
Bei Kälte ziehen sich die Muskeln zusammen.
In the cold, the muscles contract.
When talking about moving into an apartment with someone, the verb is often used with the preposition 'mit' and the dative. It can also stand without an object if it is clear who is meant.
Er ist mit seiner Partnerin zusammengezogen.
He moved in together with his partner.
In the meaning 'to become narrower' or 'to contract', the verb is always used reflexively. The subject is what becomes smaller, for example a muscle, fabric, or the pupils.
Sein Gesicht verzog sich zu einer Grimasse.
His face twisted into a grimace.
The expression 'es zieht sich zusammen' is often used impersonally to announce that a thunderstorm or bad weather is approaching. The subject can also be 'ein Gewitter' (a thunderstorm) or 'die Wolken' (the clouds).
Beeil dich, am Himmel zieht sich etwas zusammen!
Hurry up, something is gathering in the sky!
to concentrate
'konzentrieren' and 'zusammenziehen' can both mean that people, forces, or resources are gathered in one place. 'konzentrieren' sounds more general and often somewhat more factual: you can concentrate power, money, tasks, or personnel in one place. 'zusammenziehen' fits especially well when groups or forces are actively brought to one place, for example troops or emergency personnel. The words can be confused because both describe gathering things at one point. 'konzentrieren' emphasizes the central place or the bundling more, while 'zusammenziehen' emphasizes the movement toward that place more.

Vor dem Sturm zog die Feuerwehr zusätzliche Einsatzkräfte in der Stadt zusammen.
Before the storm, the fire department gathered additional emergency personnel in the city.
Die Firma konzentriert ihre wichtigsten Aufgaben jetzt in der Zentrale.
The company is now concentrating its most important tasks at headquarters.