Я отдам тебе книгу после работы.

Отдам is the 1st person singular future form of отдать.

• отдать = a perfective verb meaning to give away / hand over
• я отдам = I will give / I’ll hand over

Because отдать is perfective, it does not form the future with буду. Instead, it has a simple future form:

• я отдам
• ты отдашь
• он/она отдаст, etc.

So Я отдам тебе книгу means I will give you the book.

Because тебе is in the dative case, which is used for the recipient of something.

Compare:

• ты = you (subject form / nominative)
• тебе = to you (dative)

In this sentence, the book is being given to you, so Russian uses the dative:

• Я отдам тебе книгу = I will give you the book

Very often, English does not show to explicitly (I’ll give you the book), but Russian still uses the dative case.

Because книгу is in the accusative case, used for the direct object of the verb.

• книга = nominative singular
• книгу = accusative singular

The direct object is the thing being given: the book.

So:

• Я = subject
• отдам = verb
• тебе = indirect object / recipient
• книгу = direct object

For feminine nouns ending in -а, the accusative singular often changes to -у:

• книга → книгу
• машина → машину

Because the preposition после requires the genitive case.

So:

• работа = nominative
• работы = genitive singular

That is why Russian says:

• после работы = after work

This is something you simply need to memorize with the preposition:

• после урока = after the lesson
• после обеда = after lunch
• после фильма = after the film

Usually it means after work in a general everyday sense.

Russian often does not use a possessive like my when it is understood from context. So после работы can naturally mean:

• after work
• after I finish work
• after my workday

If you really wanted to be more explicit, you could say something like после моей работы, but that is usually less natural in an ordinary sentence like this.

Yes, it can often be omitted.

Russian verbs usually show the person clearly, so отдам already tells you the subject is I. That means both of these are possible:

• Я отдам тебе книгу после работы.
• Отдам тебе книгу после работы.

Including Я can make the subject slightly more explicit, contrastive, or simply a bit clearer in context. Russian often includes pronouns when the speaker wants emphasis, contrast, or a more complete sentence feel.

Yes. Russian word order is relatively flexible, although the neutral version here is very natural:

• Я отдам тебе книгу после работы.

Other orders are possible, but they can shift emphasis:

• После работы я отдам тебе книгу.
  Emphasis on after work
• Книгу я отдам тебе после работы.
  Emphasis on the book
• Тебе я отдам книгу после работы.
  Emphasis on to you

So the meaning stays basically the same, but the focus changes.

Both can relate to giving, but отдать often suggests handing something over, giving it back, or passing it to someone, sometimes with a sense of transfer being completed.

• дать = to give
• отдать = to hand over / give away / give back, depending on context

In many contexts, Я дам тебе книгу and Я отдам тебе книгу may both be translated as I’ll give you the book, but отдать can sound a bit more like physically passing it over or returning it.

The exact nuance depends on context.

It is informal because it uses тебе, which comes from ты.

Compare:

• тебе = to you (informal, singular)
• вам = to you (formal or plural)

So:

• Я отдам тебе книгу после работы. = informal, speaking to one person you know well
• Я отдам вам книгу после работы. = formal, or speaking to more than one person

Yes, absolutely:

• После работы я отдам тебе книгу.

This is very natural and probably one of the most common alternatives. It puts the time expression first, similar to English After work, I’ll give you the book.

Russian often moves time expressions to the front when they set the scene.

A careful pronunciation would be roughly:

• Я — ya
• отдам — at-DAM
• тебе — ti-BYE
• книгу — KNEE-goo
• после — POS-lye
• работы — ra-BO-ty

A few useful pronunciation notes:

• In отдам, the stress is on the second syllable: отдáм
• In тебе, the stress is on the last syllable: тебé
• In работы, the stress is on the second syllable: рабóты

Like many unstressed Russian vowels, some sounds are reduced in natural speech, so the written vowels do not always sound exactly as they look.

Not with the same meaning.

• Я отдам тебе книгу после работы = I will give you the book after work
  This is a single completed action
• Я буду отдавать тебе книгу после работы sounds odd here, because буду отдавать is imperfective and suggests an ongoing, repeated, or process-like action

In this context, you want a one-time completed future action, so отдам is the natural choice.

If you were talking about repeated actions, then an imperfective form could make sense in a different sentence.