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Grammar

Verb Conjugation

English Person Ending German Example
I -e ich spiele
You (singular) -st du spielst
He/She/It -t er/sie/es spielt
We -en wir spielen
You (plural) -t ihr spielt
You (formal) -en Sie spielen
They -en sie spielen

Verb Sein (to be)

German English    German  English
singular     plural  
 ich bin  I am
   wir sind
we are
 du bist
you (singular) are
   ihr seid
you (guys) are
 Sie sind
you (formal) are
   Sie sind
you (formal) are
 er/sie/es ist
he/she/it is
   sie sind
they are

Cases

The Four German Cases (link). Pronouns in four cases (link).

Changing articles with cases:
Definite Articles (the)
Fall
Case
Männlich
Masculine
Weiblich
Feminine
Sächlich
Neuter
Mehrzahl
Plural
Nom der die das die
Akk den die das die
Dat dem der dem den
Gen des der des der
Indefinite Articles (a/an)
Fall
Case
Männlich
Masculine
Weiblich
Feminine
Sächlich
Neuter
Mehrzahl
Plural
Nom ein eine ein keine*
Akk einen eine ein keine*
Dat einem einer einem keinen*
Gen eines einer eines keiner*

Source: The Four German Cases (link)

Accusative

Accusative object is the direct object in a sentence. Example: "Ich sehe mich."
See Accusative Pronouns (link) at Duolingo.

Genitive

Possessive case. See Wikipedia.

Dative

The dative object is an indirect object in a sentence. Example: Ich gebe das Buch meinem Vater. Ich gebe dir ein Buch. 
Also,  when used with mit, bis, zu, neben, etc. "Wir spielen mit der Katze."
See Dative Case (link) on DuoLingo, Wikipedia.

Contractions

Original Contraction English
an + dem am at the/on the
bei + dem beim by the/at the
zu + dem zum to the

In versus Im

'In' is a preposition which may go with either dative or accusative case. Depending on the gender of the noun that results in 'in dem', 'in den', 'in die' or 'in das'. 'Im' is a contraction of 'in dem', so that it only applies to masculine words in dative case. (Source: see here)

Nominative Pronouns

Personal Pronouns in the Nominative Case

A pronoun is a word that represents a noun, like "er" does for "der Mann." In the nominative case, the personal pronouns are simply the grammatical persons you already know: "ich," "du," "er/sie/es," "wir," "ihr," "sie," and "Sie."

Demonstrative Pronouns in the Nominative Case

The demonstrative pronouns in English are: this, that, these, and those. In German, the demonstrative pronouns in the nominative case are the same as the definite articles. That means, "der," "die" and "das" can also mean "that (one)" or "this (one)" depending on the gender of the respective noun, and "die" can mean "these" or "those." For example, if you talk about a certain dog, you could say "Der ist schwarz" (that one is black).

Links

  • German pronouns (link)
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