Different usage of の


I am familiar with the particle の. Either it be using it as in "possessive"
cases like 私の家族.

Or its usage as the word "of" like in 日本語の本.

But in this special case I can't figure it out why we use the の, and if
there's an alternative to it like in "every type" すべてのタイプ. It feels like the の
translates to "The" in the alternate translation "all the types". In the
following sentence I can use の in two different ways, can someone, please,
help me with that?

Eg: 私は音楽のすべてのタイプが好きです。




すべて means "all", "everything" and it is a word which indicates quantity and a
degree.

の has many usages and this の is used with the words which indicate quantity
and a degree.

For example, 多くの牛(many cows), 二冊の本(two books).




[This jisho entry](http://jisho.org/word/%E5%85%A8%E3%81%A6) lists すべて as a の
adjective. These types of adjectives are usually nouns which function as
adjectives when の is placed after them.

すべて normally means "everything", but すべてのX means "every X".

