about the third sentence - it seems that it is uncommon for a russian to pronounce ы after г or к in a not stressed position. Just compare - нет воды (вода - воды) и нет водки (водка - водки) fourth sentence - я вижу (кого? что?) нашего ученика - it is accusative. The two forms (accusative and genitive) are simply similar in this case (and very often generally) Я НЕ вижу (кого? чего?) нашего ученика - this is genitive.

1. У этого автора большой опыт. а) Pay attention to the spelling of the word ЭТОГО b) It's nominative. It's very common and typical grammar pattern in the Russian language with an omitted verb and a subject (a subject is always in the nominative case) at the end of the sentence. In English, the same idea would be expressed by the usage of the verb have and an inverted subject-object relation. The author has a great experience. 2. У меня много опыта. It's the genitive case. The word опыт is agreed with the word много. У меня много (чего?) опыта. So, the noun is the 2 declension type, masculine. That's why it takes the a-ending. 3. Кто автор этой книги? Книга is 1 type declension noun, so in the genitive, such type nouns take the и-ending or ы-ending. The nouns with га- endings in the nominative take the и-ending in the genitive. E.g. книга, фляга, тайга, бумага, шпага, влага, дорога, карга, Прага, Ольга, Волга. 4. Я не вижу нашего ученика. The negative particle не has nothing to do with the genitive case of the object ученик. This negative particle relates to the verb, not to the object. I do NOT (= не) see our pupil. Actually, it's very tricky sentence because when we have negation both (the accusative and the genitive) can be used. But in this particular situation (because the verb видеть is the verb of perception) we use the genitive, the ending of which for the noun ученик is the same as of the accusative. The detailed explanation on topic is here http://new.gramota.ru/spravka/letters/67-otr

1. It is nominative:) LITERALLY it is a mixture of two: "At this author experience [is] large" (or "[[there] is] large experience at this author"). Less literally: "This author has extensive experience". Semantically "у тебя" (at you) often is identical to "you have". У меня болит голова. / I have a headache "head is-acheing at me" literally. We _feel_ the same thing saying the Russian phrase:) After "у этого автора" you can say anything. "head is acheing", "experience is extensive", "it is sunny" etc. It is more flexible than Englsh 'have': "У нас тепло" - "it is warm here". In this case it is ".... is ...." construction. 'Is' is omitted in Russian. But it requires nominative. 2. "and the second one is genitive/masculine (+a) because the word много?"" Yes:) Много needs genitive. "Much OF experience". It is not accidental, genetive is often used with quantities.

I would advise you to find a theme "Падежи русского языка". There are 5 in Russian language and They are responsible for the endings of words. But also - theme "Склонение существительных в русском языке" - It's about that all the subjects in the Russian language are split into three groups - masculine, feminine and middle.

Cengiz , In the first sentence, it's nominative case, masculine, singular. It means that "there is experience" you can check yourself and say: У етого автора большой опыт - У этого автора ЕСТЬ большой опыт". The second sentence is genitive, masculine and singular. In Russian we almost never put the verb "to be" in the sentence like this. The third sentence is a feminine noun in the genitive case. It's correct and the ending must be "и". The fourth sentence is like this because of the verb вижу. The particle "не" works as a negation. Without не it would be "Я вижу нашего ученика". Itäs masculine, genitive.