
einziehen
to move in
To take up residence in a new apartment or a new house.
Nächste Woche ziehen wir endlich in die neue Wohnung ein.
Next week we are finally moving into the new apartment.
to move in / collect / absorb
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to move in
To take up residence in a new apartment or a new house.
Nächste Woche ziehen wir endlich in die neue Wohnung ein.
Next week we are finally moving into the new apartment.

to collect
To collect or forcibly levy money, debts, taxes, or contributions.
Der Mitgliedsbeitrag wird monatlich per Lastschrift eingezogen.
The membership fee is collected monthly by direct debit.

to absorb
To be absorbed by a material; to penetrate into something and become part of it.
Lass die Handcreme erst vollständig einziehen.
Let the hand cream absorb completely first.

to confiscate
To officially take away or confiscate something, such as a driver's license, a weapon, or goods.
Nach der Geschwindigkeitsüberschreitung hat die Polizei seinen Führerschein eingezogen.
After the speeding violation, the police confiscated his driver's license.

to enter
To arrive at a place ceremonially or in formation; to march into a city.
Die Gladiatoren zogen unter dem Jubel der Menge in die Arena ein.
The gladiators entered the arena to the cheers of the crowd.

to draft
To oblige someone to do military service or war service.
Mein Großvater wurde 1942 zur Wehrmacht eingezogen.
My grandfather was drafted into the Wehrmacht in 1942.

to thread
To guide a thread, ribbon, or elastic band through an opening or casing made for it.
Ich muss ein neues Gummiband in meine Jogginghose einziehen.
I need to thread a new elastic band through my sweatpants.
'Einziehen' (to move in / collect / absorb) is a separable verb. The prefix 'ein-' stands at the end of the main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Meine neuen Nachbarn ziehen morgen ein.
My new neighbors are moving in tomorrow.
The verb consists of 'ein-' (in, into) and 'ziehen' (to move, to pull something). The literal meaning 'hineinziehen' (to pull into) or 'hineinbewegen' (to move into) helps you understand many of the figurative meanings, e.g. into an apartment, into the skin, or into an organization.
Die Soldaten zogen in die eroberte Stadt ein.
The soldiers entered the conquered city.
The perfect tense is formed with 'sein' (to be) when movement of the subject is meant, e.g. moving into a house or cream being absorbed. In the other meanings, such as money, driver's license, or military, 'haben' (to have) is used.
Wir sind letztes Jahr in dieses Haus eingezogen.
We moved into this house last year.
When someone moves into a new place to live, the preposition 'in' is used with the accusative. Typical formulations are 'in eine Wohnung einziehen' (to move into an apartment) or 'in ein Haus einziehen' (to move into a house).
Sie ist gerade in ihre erste eigene Wohnung eingezogen.
She has just moved into her first apartment of her own.
In this meaning, 'einziehen' (to collect) is usually combined with financial or administrative terms. Typical objects are 'Schulden' (debts), 'Steuern' (taxes), 'Gebühren' (fees), or 'Forderungen' (claims).
Das Finanzamt wird die ausstehenden Steuern einziehen.
The tax office will collect the outstanding taxes.
In the meaning 'absorbiert werden' (to be absorbed), the verb is often used without an object. The subject is the substance that penetrates into a surface.
Die Sonnencreme zieht schnell ein und fettet nicht.
The sunscreen absorbs quickly and is not greasy.
This meaning is typical of official language. The subject is usually an authority such as the police or customs, which officially takes something away.
Der Zoll hat die gefälschten Markenprodukte eingezogen.
Customs confiscated the counterfeit branded products.
In the context of military service, 'einziehen' (to draft) is very often used in the passive to say that someone was required to serve. The construction is: 'jemand wird (zum Militär) eingezogen' (someone is drafted into the military).
Er wurde direkt nach der Schule zum Wehrdienst eingezogen.
He was drafted into military service right after school.
to refer / move into / receive
Beziehen and einziehen can both describe the beginning of living in a new place. With beziehen, the apartment is the direct object and is emphasized more as the new residence; einziehen focuses more on the process and usually names the destination with in.

Am ersten Mai ziehen wir in unsere neue Wohnung ein.
On May 1, we are moving into our new apartment.
Am ersten Mai beziehen wir unsere neue Wohnung.
On May 1, we are moving into our new apartment.