Ik leg het boek erop.

Because leggen is the infinitive, meaning to lay / to put down.

In this sentence, the verb is conjugated for ik in the present tense:

• ik leg
• jij legt
• hij/zij/het legt
• wij/jullie/zij leggen

So Ik leg het boek erop means I put / I lay the book on it.

This is a very common Dutch question.

• leggen = to lay / to put something somewhere
  
  • it is transitive, so it takes an object
• liggen = to lie / to be lying somewhere
  
  • it describes the position of something

Compare:

• Ik leg het boek erop. = I put the book on it.
• Het boek ligt erop. = The book is lying on it.

So if you cause the book to go there, use leggen. If you describe where the book already is, use liggen.

Erop is a pronominal adverb: er + op.

Dutch often uses this structure instead of repeating a noun after a preposition.

For example:

• op de tafel = on the table
• later, instead of repeating op de tafel, Dutch can say erop = on it / on there

So erop refers back to something already known from context.

Other common examples:

• erin = in it
• eruit = out of it
• eraan = on it / attached to it
• ervoor = in front of it / for it

Because in Dutch, er + preposition usually forms one written word when it functions as a pronominal adverb.

So you write:

• erop
• erin
• eronder
• ervoor
• ermee

Not er op in this kind of use.

That is just the normal spelling rule for this construction.

Because that is the natural Dutch word order here.

The sentence structure is:

• Ik = subject
• leg = finite verb
• het boek = direct object
• erop = adverbial/prepositional element

Dutch main clauses often place the finite verb in second position, and other elements like erop often come later in the clause.

So:

• Ik leg het boek erop.

sounds natural.

For an English speaker, it may feel more natural to expect something like I put the book on it, where on it also comes at the end. So in this case Dutch is actually fairly similar.

Not in this sentence.

The verb here is simply leggen.
Erop is a separate element that tells you where the book is being put.

So this is:

• leggen
  • erop

not a single verb.

This matters because Dutch also has real separable verbs, and learners sometimes confuse them with structures like this.

For example, opleggen is an actual verb, but it usually means something like to impose or to assign, which is different.

So in Ik leg het boek erop, think of erop as a location phrase, not as part of the verb itself.

Because boek is a het-word in Dutch.

Dutch nouns are either:

• de-words
• het-words

Boek is neuter, so its singular definite article is het:

• het boek = the book

You simply have to learn the article with the noun.

Useful related forms:

• een boek = a book
• het boek = the book
• de boeken = the books

Notice that the plural becomes de, even though the singular is het.

No, not in normal Dutch.

When English says on it, Dutch usually uses a pronominal adverb such as erop, not op het.

So:

• Ik leg het boek erop. = correct
• Ik leg het boek op het. = generally not correct for this meaning

Dutch prefers:

• op de tafel if you name the thing
• erop if you refer back to it

This is one of the big differences between English and Dutch.

Yes, but then het usually refers to the thing being placed, not the book specifically.

For example:

• Ik leg het boek erop. = I put the book on it.
• Ik leg het erop. = I put it on it.

So het boek can be replaced by het if the object is already clear from context.

What you usually cannot do is scramble the sentence into something like:

• Ik leg erop het boek.

That sounds unnatural in ordinary Dutch.

In a subordinate clause, the conjugated verb goes to the end.

So:

• main clause: Ik leg het boek erop.
• subordinate clause: ... dat ik het boek erop leg.

Example:

• Ik zeg dat ik het boek erop leg.
  = I say that I put the book on it.

This is a useful pattern to notice, because Dutch word order changes a lot between main clauses and subordinate clauses.

Sometimes, but not always.

Dutch often distinguishes between:

• leggen = putting something down so that it lies
• zetten = putting something down so that it stands

With a book, the choice depends on how it is placed:

• Ik leg het boek erop. = I lay the book on it, probably flat
• Ik zet het boek erop. = I put the book on it standing upright, or in some contexts just place it there

So leggen is a good choice if the book is being laid down rather than stood up.