What is the meaning of "老师会介绍我们认识的,"? Why is the 的 at the end of the sentence?
'A new book' is translated into 一本新书. Why isn't it 一本新的书 just like in 一本蓝色的书?
已经 vs. 了?
Does anyone know a website that has all kinds of measure words in Chinese like yi1 ben3, yi1 bei1?
1 . Here the 的 is a structural particle and its function is to nominalize the phrase or clause before it.
However, this sentence structure probably does not exist in English.
To better explain it I change the sentence to another one: 苹果派很好吃 Apple pies are delicious (translate it to very delicious if you like, which is not important here).
Imagine I am a Chinese who has never seen an apple pie. Here is our conversation:
You: 你吃过苹果派吗？Have you ever eaten an apple pie?
You: 苹果派很好吃 的! Apple pies are delicious! (A)
你应该尝尝。You should try it.
Then we go to eat apple pie.
You: 苹果派好吃吗？Is apple pie delicious?
Me: 苹果派很好吃! Apple pie is delicious! (B)
In (A), what you are doing is to make an assertive statement on a truth (at least you think it is). You can imagine that behind the Chinese sentence you say, a phrase such as The fact is..., The truth is..., is hidden.
In (B), I am only talking about my personal opinion, it suffice to use a simple affirmitive statement.
Let's go back to a simple example that you might have learned before:
这支笔是什么颜色 的？What colour is this pen?
这支笔是红 的 。This pen is red.
These 2 sentences are respectively literally:
This pen is a pen of what colour?
This pen is a red one.
The function of 的 in these sentences are the same as in yours.
Finally what the meaning of 老师会介绍我们认识的 is. Since there is no context, my impression is, the speaker and the listener have the same teacher, but they do not know each other (so it is amazing then why this sentence will be said), and the speaker believes that the teacher will introduce them to each other. Other than this, I have no idea without knowing the context behind, given an opportunity that it may be a misuse.
2 . We omit 的 when we want a close integration of the attributive and the noun. 一本新的书 would usually just mean the book is not old, as you would use when you say I lost my book and my mom bought me a new book 我把书丢了，我妈妈给我买了一本新的书; 一本新书 would ususally mean a newly published book, as you would use when you say The author has written a new book 作者写了一本新书。Again, there is no absolute rule here and the best use depends on the context.
3 . Ref. other users' explanation made.
4 . The list in Wikipedia should be good enough, no?
On (2): as I understand, "新" (to be new) and "蓝" (to be blue) are stative verbs, and when you use those as an adjective they can stand by themselves. The "蓝色" ("blue color") is a noun, so it cannot stand in the place of an adjective, and needs "的" to turn it into an adjectival thing ("of a blue color"). Likewise for "新". I think "一本新书" would also be valid, but that e.g. "蓝色的书" makes it clearer that you are talking about the color literally. Cf. how in USA English "blue book" could refer to a car's Blue Book value (Kelley's), but "a blue-colored book" just means a book of that color.
(My Mandarin is not that great yet so someone please correct me if this is wrong.)