Learn Hardcore Russian: В библиотеке можно читать любую книгу.

The preposition в (in) indicates location and requires the prepositional case when the action is static. Since библиотека is a feminine noun, its prepositional singular form is библиотеке. Together в библиотеке means “in the library.”

What does можно mean, and why is it used here?

Можно is an impersonal modal word that expresses permission or possibility (“it is possible,” “one may”). In this sentence, it tells us that reading any book is allowed or possible in that place.

Why do we use the infinitive читать after можно?

After можно, Russian always uses the infinitive form of the verb to show the action that is permitted or possible. That’s why we say читать (to read) rather than a conjugated form.

Why is любую книгу in the accusative case?

Любую книгу is the direct object of the verb читать. Feminine singular nouns take the accusative ending -ую for adjectives and -у for nouns, so любая книга becomes любую книгу.

Could we use каждую книгу instead of любую книгу, and how would the meaning change?

Yes. Можно читать каждую книгу would mean “one may read every (each) book,” emphasizing that you can read each book one by one. Можно читать любую книгу emphasizes “any book at all,” focusing on the freedom to choose.

Why is there no explicit subject in this sentence?

This is an impersonal construction with можно. There is no personal subject (I, you, we) because the permission or possibility is general or applies to anyone, so Russian drops the subject.

Can we change the word order, for example, putting можно at the end?

Russian word order is flexible. You could say:

Можно читать любую книгу в библиотеке.
В библиотеке любую книгу можно читать. All mean essentially the same, though the original order is the most neutral.

What’s the difference between читать and прочитать here?

Читать is imperfective, stressing the process or general ability (“to read”). Прочитать is perfective, focusing on completing the action (“to read through/to finish reading”). With можно, можно прочитать любую книгу would imply you can finish reading any book, while можно читать любую книгу simply says you may read any book (not necessarily finish it).