Norwegian nouns are inflected for number (singular/plural) and for definiteness (indefinite/definite). In a few dialects, definite nouns are also inflected for the dative case.
Norwegian nouns belong to three noun classes (genders): masculine, feminine and neuter. All feminine nouns can optionally be inflected using masculine noun class morphology in Bokmål due to its Danish heritage. In comparison, the use of all three genders (including the feminine) is mandatory in Nynorsk.
In general, the genitive case has died out in modern Norwegian and there are only some remnants of it in certain expressions: til fjells (to the mountains), til sjøs (to the sea). To show ownership, there is an enclitic -s similar to English -'s; Sondres flotte bil (Sondre's nice car, Sondre being a personal name). There are also reflexive possessive pronouns, sin, si, sitt, sine.
There are three indefinite articles (a or an) that correspond with Norwegian genders: en for masculine nouns, ei for feminine nouns and et for neuter nouns. The majority of nouns in Norwegian are masculine, so they take the indefinite article en.
The definite article (the) is not a separate word like in most other languages. It is simply a form of the indefinite article attached to the end of the noun. For feminine nouns, the definite article that is attached to the noun is -a.
en mann (a man) - mannen (the man)
ei fru (a woman) - frua (the woman)
et hus (a house) - huset (the house)
In theory, the female gender does still exist in Bokmål, but in practice, it is rarely used and the feminine nouns, as mentioned previously, are inflected like masculine nouns, i.e. add -en instead of -a for the definite form.
Norwegian adjectives, like those of Swedish and Danish, inflect for definiteness, gender, number and for comparison(affirmative/comparative/superlative). Inflection for definiteness follows two paradigms, called "weak" and "strong", a feature shared among the Germanic languages.
In Norwegian, a definite noun has a suffixed definite article (see above). However, when a definite noun is preceded by an adjective, the adjective also gets a definite inflection.
grønne (definite) - grønn (indefinite)
There is also another definite marker den (den for masculine and feminine, det for neuter) that has to agree in gender with the noun when the definite noun is accompanied by an adjective. It comes before the adjective.
Det grønne eplet (The green apple)
Adverbs can be formed from adjectives in Norwegian. English usually creates adverbs from adjectives by the suffix -ly, like the adverb beautifully from the adjective beautiful.
By comparison, Scandinavian languages usually form adverbs from adjectives by using the grammatical neuter singular form of the adjective. This is in general true for both Bokmål and Nynorsk.
Det er grusomt (It is terrible)
Han er grusomt treig (He is terribly slow)
Norwegian personal pronouns are declined according to case: nominative/accusative. Like English, pronouns in Bokmål and Nynorsk are the only class that has case declension. Some of the dialects have also preserved some form of the dative in nouns.
There are personal pronouns (jeg, du), possessive pronouns (min, din), demonstrative pronouns (denne, dette), reflexive pronouns (meg, deg).
Norwegian verbs are not conjugated for person or number unlike English and most European languages, though a few Norwegian dialects do conjugate for number.
Norwegian verbs are conjugated according to mainly three grammatical moods: indicative, imperative and subjunctive, though the subjunctive mood has largely fallen out of use and is mainly found in a few common frozen expressions.
Indicative verbs are conjugated for tense: present/past/future. The present and past tense also have a passive form for the infinitive.
Norwegian word order - SVO - is generally more like English than German. However, if an element is fronted (moved to the first position in the sentence) it displaces the subject, which moves behind the verb.
Jeg må visst gå hjem nå. (I’d better go home now.)
Here nå (now) is fronted: Nå må jeg visst hjem. (Now I'd better go home.)
Norwegian has a complex system of prepositions that may also be used differently in different dialects. Unfortunately, there is no rule that will help you master them: they can be mastered through regular practice only.
The most common prepositions in Norwegian are: after (etter), before (før), between (mellom), under (under), on (på or oppå), in (i), outside (utanfor), behind (bak).
This is a very brief overview of Norwegian grammar. To truly master it, you will need to study each of the parts of speech in much more detail. However, this overview will hopefully give you a general idea of the Norwegian grammatical system and of the main points you should consider when learning.