
vertraut
familiar
Well-known and familiar, so that you feel safe and comfortable with it.
Der Geruch von frisch gebackenem Kuchen ist mir sehr vertraut.
The smell of freshly baked cake is very familiar to me.
familiar
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familiar
Well-known and familiar, so that you feel safe and comfortable with it.
Der Geruch von frisch gebackenem Kuchen ist mir sehr vertraut.
The smell of freshly baked cake is very familiar to me.

intimate / familiar
Describing a close, personal relationship between people that is shaped by mutual trust.
Die beiden unterhielten sich in einem sehr vertrauten Ton.
The two of them spoke in a very intimate tone.

to be/become familiar with
To have or acquire good knowledge of something.
Bevor Sie die Maschine benutzen, sollten Sie sich mit der Anleitung vertraut machen.
Before you use the machine, you should familiarize yourself with the instructions.
The adjective 'vertraut' (familiar) is closely related to the noun 'das Vertrauen' (trust). A person or thing that is 'vertraut' to you is one that you know well and trust.
Sie hat nur wenige, aber sehr vertraute Freunde.
She has only a few, but very close friends.
If you want to express to whom something is familiar, that person is in the dative. The structure is: [thing in the nominative] + ist + [person in the dative] + vertraut.
Diese Melodie ist mir irgendwie vertraut.
This melody is somehow familiar to me.
In this meaning, 'vertraut' (intimate/familiar) describes a close, personal relationship between people. It is often used to characterize an atmosphere or an interaction.
Die beiden Kollegen pflegen einen sehr vertrauten Umgang miteinander.
The two colleagues have a very familiar way of interacting with each other.
The construction 'sich mit etwas vertraut machen' (to familiarize oneself with something) is a fixed expression. It always uses the reflexive pronoun in the accusative ('sich') and the preposition 'mit' followed by the dative.
Ich muss mich erst mit der neuen Software vertraut machen.
I first have to familiarize myself with the new software.
known
A place is bekannt (known) as soon as you have seen or experienced it before. It usually feels vertraut (familiar) only after you have become more accustomed to it, so that you feel safe and comfortable there. Vertraut therefore expresses more personal closeness here than bekannt.

Der Bahnhof ist mir vertraut, weil ich seit Jahren täglich hier umsteige.
The train station feels familiar to me because I have been changing trains here every day for years.
Der Bahnhof kommt mir bekannt vor, weil ich schon einmal hier war.
The train station seems familiar to me because I have been here once before.