Genitive "-'s" or "of"

“Takeshi’s mother” or “the mother of Takeshi” (Noun)

mother --> okaasan（おかあさん）
Takeshi --> Takeshi-san (たけしさん)

Key 1: "‘s" or "of" --> no（の）

Key 2: The /no/-marked noun, the former noun in "[noun]-/no/ [noun]", describes the head noun by specifying the 1) possessor, 2) the whole side of a whole-part relation, [3) the attribute, of the head noun, or 4) the subject or object of the noun if the noun is an event-describing noun, as we learn later for the third and fourth meanings].

1)                                             okaasan           (Noun)
    A modifying phrase occurs before the modified form in Japanese, i.e., okaasan in this example.
    The noun okaasan ‘mother’ need a person that she is a mother of, i.e., a child whether it is implicit or explicit.

2) Takeshi-san-no okaasan (Noun)
たけしさんの　おかあさん

N.B.) Noun-/no/ noun as a whole is a noun. Thus, noun-/no/ noun grammatically occurs wherever a noun occurs.