Learn Dutch: Ik geef hem het boek. - I am giving him the book.

In Dutch, when a sentence has both an indirect object (the receiver, hem) and a direct object (the thing being given, het boek), the indirect object comes first. This matches the English structure perfectly: 'I give him the book'.

Could I use the word aan (to) here, like 'I give the book to him'?

Yes! You can say Ik geef het boek aan hem. Notice that when you add the preposition aan, the direct object (het boek) moves in front of the indirect object phrase (aan hem).

The translation says 'I am giving'. Why doesn't the Dutch sentence use the aan het continuous form?

Dutch uses the simple present tense (ik geef) much more often than English uses 'I give'. While you technically can use the continuous form (Ik ben hem het boek aan het geven), it sounds a bit unnatural for a quick, momentary action like handing someone a book.

I sometimes mix up de and het. Why is it het boek?

Boek is a neuter noun, so it takes het. While there are rules for some words (like diminutives always taking het and plural words always taking de), for a standard base noun like boek, the gender simply has to be memorized.