
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.

to contract
To become narrower, smaller, or to contract, as for example a muscle, fabric, or the pupils.
Bei Kälte zieht sich die Haut zusammen und man bekommt eine Gänsehaut.
In the cold, the skin contracts and you get goose bumps.

to draw together
To close something or make it tighter by pulling, for example curtains or a drawstring bag.
Bitte zieh die Vorhänge zusammen, die Sonne blendet.
Please draw the curtains together; the sun is glaring.

to gather
Describes clouds gathering in the sky, often announcing a storm.
Am Horizont zieht sich ein Gewitter zusammen.
A thunderstorm is gathering on the horizon.

to concentrate
To gather or concentrate forces, troops, or people in one place.
Der General befahl, alle verfügbaren Einheiten an der Front zusammenzuziehen.
The general ordered all available units to be concentrated at the front.
'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 draw closed / move in
Zuziehen and zusammenziehen can both be used when closing something with a pulling motion. Zuziehen emphasizes that something is being closed. Zusammenziehen emphasizes more strongly that the material is gathered or made tighter in the process.

Sie zog den Vorhang zusammen, sodass der Stoff in dichten Falten hing.
She pulled the curtains together, leaving the fabric in tight folds.
Sie zog den Vorhang zu, damit kein Licht ins Zimmer fiel.
She drew the curtain closed so that no light entered the room.