What function and structure is attributed to "de" in Mandarin grammars?
A. Basis for the question: In the simplest cases (e.g., "wo3de che1", "che1 de sùdù"), "de" seems to correspond to a marker of "genitive case" like the "Saxon genitive -s" or the preposition "of" in English (which include "possessive" and several other meanings). However, "de" can also intervene between adjectival phrases and their nouns (cf. "hen3 guì de che1" = very expensive car), where the expression of genitive case/possession is not a possible function. More generally, "de" also intervenes between incomplete clauses and nominals, e.g., in "wo3 xi3huan __ de che1" = car that I like (where it resembles an English relative pro-noun in object function), or in "mài shu1 de rén" = person who sells books (where it resembles an English relative pronoun in subject function). So, "de" also allows the combination of an incomplete clause with a nominal that "completes" the clause, but subordinating the clause to the noun, as a modifier.
B. Preview of the question: On the whole, then, the function of "de" seems to be to make phrases of all kinds modifiers of nouns, but HOW, exactly? WHAT is the STRUCTURE of the X DE Y combination?
C. Further clarification: In other languages, let's say English, the attachment of phrases as modifiers of nouns is alternatively achieved mainly by 1) case inflections (e.g., 's), 2) prepositions (e.g., "of"), 3) relatives (who, that, whose...), and 4) participial inflections, (sleepING beauty, beauty = subject; whippING boy, boy = object; appointED officers, officers = subject). These are different grammatical resources, but they have ONE thing in common: ALL SUCH MARKERS STRUCTURALLY BELONG TO THE MODIFIER, NOT THE NOUN. Hence, 's is attached to the noun "Bill" in "Bill's+car" (NOT *Bill+s'car), the preposition "of" belongs to the PP in "the speed of the car" (i.e., speed + [of the car], not *[speed of]+ the car), the relatives "who" and "that" belong to the clauses, not to the nouns, in "the person +[who sells books]" and "the car +[that I like]" (the structure is not *[the person who] + sells books, or *[the car that] + I like).
Thus, summarizing:

QUESTION A: IS MANDARIN "DE" A GENERAL PURPOSE MARKER OF MODIFICATION?
QUESTION B: IS IT ATTACHED TO THE MODIFIER OR TO THE NOUN MODIFIED? (or, in other words: is the structure= [X+DE] + noun, OR is it = X + [DE+noun]? WHAT DO STANDARD GRAMMARS OF MANDARIN SAY ABOUT THIS?

Thank you, Italki speakers of Mandarin!Sorry, I forgot, and Lucy has just reminded me, that "de" also mediates between adverbial phrases and the verbs they modify. Please, extend my question to such cases: "de" is needed between V(P) and AdvP, but is it attached to the Adverb Phrase (...wo3 shuo1 +[de bù hao3]) to allow it to modify the VP, or is it attached to the VP to allow it to be modified by the adverbial? Of course, in other languages, adjectives and adverbs are inherently natural modifiers of nouns and verbs, respectively, and need no "adapter" to play that role. Apparently Mandarin "de" can also be omitted provided the modifiers are not phrases but monosyllabic words like "guì" or "hao3". How do standard grammars present that fact? What is supposed to allow "de" to be left out?

Thank you, dear Italkiers!

Question

What function and structure is attributed to "de" in Mandarin grammars?
A. Basis for the question: In the simplest cases (e.g., "wo3de che1", "che1 de sùdù"), "de" seems to correspond to a marker of "genitive case" like the "Saxon genitive -s" or the preposition "of" in English (which include "possessive" and several other meanings). However, "de" can also intervene between adjectival phrases and their nouns (cf. "hen3 guì de che1" = very expensive car), where the expression of genitive case/possession is not a possible function. More generally, "de" also intervenes between incomplete clauses and nominals, e.g., in "wo3 xi3huan __ de che1" = car that I like (where it resembles an English relative pro-noun in object function), or in "mài shu1 de rén" = person who sells books (where it resembles an English relative pronoun in subject function). So, "de" also allows the combination of an incomplete clause with a nominal that "completes" the clause, but subordinating the clause to the noun, as a modifier. 
B. Preview of the question: On the whole, then, the function of "de" seems to be to make phrases of all kinds modifiers of nouns, but HOW, exactly? WHAT is the STRUCTURE of the X DE Y combination?
C. Further clarification: In other languages, let's say English, the attachment of phrases as modifiers of nouns is alternatively achieved mainly by 1) case inflections (e.g., 's), 2) prepositions (e.g., "of"), 3) relatives (who, that, whose...), and 4) participial inflections, (sleepING beauty, beauty = subject; whippING boy, boy = object; appointED officers, officers = subject). These are different grammatical resources, but they have ONE thing in common: ALL SUCH MARKERS STRUCTURALLY BELONG TO THE MODIFIER, NOT THE NOUN. Hence, 's is attached to the noun "Bill" in "Bill's+car" (NOT *Bill+s'car), the preposition "of" belongs to the PP in "the speed of the car" (i.e., speed + [of the car], not *[speed of]+ the car), the relatives "who" and "that" belong to the clauses, not to the nouns, in "the person +[who sells books]" and "the car +[that I like]" (the structure is not *[the person who] + sells books, or *[the car that] + I like). 
Thus, summarizing:

QUESTION A: IS MANDARIN "DE" A GENERAL PURPOSE MARKER OF MODIFICATION?
QUESTION B: IS IT ATTACHED TO THE MODIFIER OR TO THE NOUN MODIFIED? (or, in other words: is the structure=  [X+DE] + noun, OR is it =  X + [DE+noun]? WHAT DO STANDARD GRAMMARS OF MANDARIN SAY ABOUT THIS?

Thank you, Italki speakers of Mandarin!Sorry, I forgot, and Lucy has just reminded me, that "de" also mediates between adverbial phrases and the verbs they modify. Please, extend my question to such cases: "de" is needed between V(P) and AdvP, but is it attached to the Adverb Phrase (...wo3 shuo1 +[de bù hao3]) to allow it to modify the VP, or is it attached to the VP to allow it to be modified by the adverbial? Of course, in other languages, adjectives and adverbs are inherently natural modifiers of nouns and verbs, respectively, and need no "adapter" to play that role. Apparently Mandarin "de" can also be omitted provided the modifiers are not phrases but monosyllabic words like "guì" or "hao3". How do standard grammars present that fact? What is supposed to allow "de" to be left out?

Thank you, dear Italkiers!

Answer

Wow! That's very sensitive of you to notice the magic "de" in Chinese!My foreign friends are unavoidably crazy about that! Here I'd have to clarify first:
There are three "de" in Chinese! What you are talking about is the "的" that combines Adj.(or the phrase and incomplete sentence used as adj. function) and n.

the simplest way of using "de" is  adj.+n.
then in English we say  a car that my mother bought for me is very nice
In Chinese we say   My mother bought for me+的de+car is very nice
Here (my mother bought for me) acts as an adj. to describe the car.

In chinese the basic sentence structure is  Subject+ Adv.(or some phrases act as Adv)+ Verb or Verb Phrases.
For example, I like the car my mother bought for me very much.
In chinese we say:
I(Subject)+very much(adv.)+like the car(Verb Phrase)
and where to put the that my mother bought? Just use "de"
I very much like my mother bought for me 的（de） car.


And you say: What part can we leave out? I notice that you say a sentence:
wo shuo de bu hao!
here It involves another "de" this "得"
when use this "de withou tone",we must know the rule of this "de"
Verb+得(de- another different "de")+ Adj
=Verb+ Adv.

In Chinese the adj and adv is the same. so how to use the adj as a adv?
There are two sayings in Chinese to express that I do something+ adv.
1. I do something do 得(de) adj
2  I something do 得（de）adj
so you can say 1,wo Chinese shuo de bu hao 2. wo shuo Chinese shuo de bu hao.

What to leave out? the thing everybody definitely know or mentioned before!!!
For you at first it's better to keep the whole part! then you can try to leave out some part and let some Chinese help you to correct!

Blablabla So much.Hope it can help you a little! I'm studying teaching chinese as a second language you can contact me! I'd like to find problems and help!!!!

Answer

“De” is regarded as a structural particle placed between attributive und head, to indicate possessive, modification, etc and can be used as modal particle;

Answer

I have to thank you again Luis for your distinctive way of asking questions.
I am always confused about the various usages of 'de' as well.
YaoYao's answer is very informative indeed and I hope to see more detailed answers supported by examples in Chinese language.

Answer

one is "的"，it's adj ,and the other is " 地" its usage  like english 
''

Answer

There are two type of "de" in Mandarin, one is adj , the other is adv. We usually use them to connect the adj words to noun words, or connect adv words to verb words.
sorry, my english is not very good , i hope you can understand.