Do you mean the declensions for accusative case? If not, I have no idea what "accusative case words" are. The only difference between nominative and accusative definite articles is the masculine case where accusative is den and nominative is der. Also, the indefinite article for masculine accusative case simply has the -en suffix.
The comments have some good explanations, so please read them if you haven't already. Duolingo also has lesson tips pages too, if you use the web version and scroll down before starting the exercises. The first lesson teaches you that nouns have gender and you need to match other words to the gender. That's all you need to understand ein Buch in this sentence. Then the lesson on 'accusative case' tells you when to use einen.
Well, there are two things affecting the ending of "ein" - grammatical gender as well as case.
Each noun (if you didn't know this already) has a grammatical gender - feminine, masculine, or neuter. The definite (words like "the" - die, der, das, den, dem) and indefinite (words like "a" - ein, einen, eine, einem) articles in front of a word change due to the grammatical gender.
Each noun is also assigned a "case" in German, depending on its function in a sentence. There are four cases - nominative, accusative, dative, and genitive. In English these aren't as important, but they change the articles in German.
In nominative case, where the noun is the subject of the sentence (the noun doing the action of the sentence), the articles are as follows:
Masculine - der, Feminine - die, Neuter - das, Plural - die
Masculine - ein, Feminine - eine, Neuter - ein, Plural - (k)eine (you can't have "a" before a plural noun in German, just like in English)
In accusative case, where the noun is the direct object of the sentence (the noun that the action of the sentence is being done to), the articles are like this:
Masculine - den, Feminine - die, Neuter - das, Plural - die
Masculine - einen, Feminine - eine, Neuter - ein, Plural - (k)eine
Dative case has to do with the indirect object of the sentence, which is harder to explain, and you won't need this this early on in the lessons, but here are the articles:
Masculine - dem, Feminine - der, Neuter - dem, Plural - den
Masculine - einem, Feminine - einer, Neuter - einem, Plural (k)einen
Genitive case isn't nearly as common, and is kind of like a possessive case. You can read more about it in the wikipedia article I'm linking.
Maybe this was overkill, but I hope it helps!
The verb is lesen, yes. But it's not du lest.
Some verbs change -e- to -i- or -ie- in the du and er, sie, es forms; this is one of them.
So we say du liest and er liest.
Two other common verbs that do this are geben "to give" and essen "to eat": we say du gibst and er gibt, du isst and er isst.
But the ihr form has the regular vowel -e-: ihr lest; ihr gebt; ihr esst.
There is no difference. Both are grammatically correct translations.
There is a present participle case for all verbs, including lesen "lesend." But no one would say "Du bist ein Buch lesend."
The present participles in German are used when forming adjectives and adverbs. - http://german.about.com/library/bladj_particip03.htm
The conjugation. It's like asking what the difference is between "am" and "are" in English: the answer is that they match together with different pronouns: "I am", "you are".
In German, liest matches with du (and some others). But lesen matches with wir (and some others). You can see the full list on sites like Canoo.net.
Can we replace liest with lest?
No. It's always du liest.
lest would be for ihr lest (you -- several people -- are reading).
lesen is one of those verbs where the stem vowel changes from -e- to -ie- in the du and er/sie/es verb forms:
- ich lese
- du liest
- er/sie/es liest
- wir lesen
- ihr lest
- sie/Sie lesen
Similarly with sehen - du siehst, er sieht, ihr seht, for example. And with a different vowel change: geben - du gibst, er gibt, ihr gebt.
Whether a verb changes the vowel like that is something you have to learn; you can't guess just from looking at the verb. For example, stehen has du stehst and leben has du lebst.
Because lessen means read and liest means reading.
lessen isn't a word.
The dictionary form is lesen. Which form you use in a sentence depends on the subject:
- ich lese = I read / I am reading
- du liest = you [one person] read / you [one person] are reading
- er/sie/es liest = he/she/it reads / he/she/it is reading
- wir lesen = we read / we are reading
- ihr lest = you [several people] read / you [several people] are reading
- sie lesen = they read / they are reading
Here, the subject is du and so we use du liest.