What are some rules governing the nominal cases in German? [duplicate]

Question

I would like to know if this sentence I have conjured up is grammatically correct or not, in particular regarding the case of the noun that follows the preposition über. As far as I have worked it out, the accusative case refers to direct objects and the dative case to indirect ones. Yet, in such sentences as what I have posted here, the prepositional phrase '' about the history of Germany'' acts as a post modifier for the direct object of the sentence ''Book.'' So obviously ''Buch'' is in the accusative case, but are we to modify what ever noun head in a prepositional phrase such as " .....für meine Schwester'' with the accusative case? or should it be Dative since the verb has ist own direct object aready?

• Ich möchte ein Buch über der Geschichte von Deutschland lesen.

Do we consider the case of nouns following prepositions like über dative or accusative?

Answer 1

In German preposition are non-local (what the position of the particles in the sentence concerns), that is, they are quite often also linked to a verb, and you learn instead of the pair

(Preposition, Case [i.e. nominative, genitive, dative or accusative])

the triple

(Verb, Preposition, Case)

Example. In your example über goes with accusative.

(lesen, über, accusative)

whence

...über die Geschichte ... lesen

Can you complete the sentence? :)

Compare:

Ich spreche über den Tisch (says the topic I talk about)

with

Ich spreche über dem Tisch (says something about my location, while I speak)

Answer 2

You need to distinguish between two sets of rules.

1) Which case do I use if my noun is connected via preposition

2) Which case do I use if my noun is NOT connected via preposition

Both sets of rules have zero to do with one another. In fact, trying to find connection may lead to confusion. The noun in question is "History (of Germany)" and as you said it's connected via the preposition "über". The question whether the verb has a direct object or not is absolutely irrelevant.
What matters is the preposition and a possibly associated verb (in this case for example "schreiben" because "über" is the preposition you use to connect a topic to the activity of writing... and "history" is a topic here).

So you need to consult the set of rules for which case to use after a preposition. Since "über" is a two way preposition you still have to decide between Dative and Accusative. In case of topics it's Accusative - for no particular reason. Many abstract uses like this one tend to go with Accusative. The Dative would be interpreted in a more literal local sense.