Использование "я" и "мне"

Question

I'm having difficulty understanding when to use "Я" and when to use "мне". In the sentence:

Я хочу книгу

We use "Я" meaning I. But in the sentence:

Мне нужна книга

We use "Мне" meaning I. Why don't we use "Я"?

Answer 1

The trick here is to note what the subject of the sentence is. In Мне нужна книга the subject is, actually, книга. Hence, книга is in the nominative case, and мне is in the dative case. The subject is the thing that is necessary, and not the person to whom it is necessary.

In Russian you see such forms quite often. Consider this:

Мне нравится эта книга.

I like this book.

Same idea: in the Russian sentence the book is the subject.

Answer 2

Мне actually means "to me" and is in the dative case, whereas я means "I" and is in the nominative case.

To review:

The nominative is the case of the subject of the sentence. In this case я: The accusative is the case of the direct object - in this case книга ➝ книгу.

Я хочу книгу.

The dative is the case of the indirect object, i.e. the recipient - in this case я ➝ мне:

Мне нужна книга. (literally: to me (is) necessary (a) book)

Answer 3

The reason behind the inversion in your second example is that нужна is not a verb (need). It is a modal predicative construction similar to adjective. So, in English it would be close to a book is necessary to me. And to me is мне.

In practice you need to know these constructions by heart, but I guess identifying the parts of speech would help.

Answer 4

Once again, don't have the rep to add a comment to @CocoPop answer, this is only meant as an addition to what's already said:

Я хочу книгу.

I want a book.

or

Мне нужна книга.

I need a book ( literally: [Myself | to me] needs [a] book )

or

Я нуждюсь в книге.

I am in need of a book.