Remember: If in the affirmative phrase, there is an indefinite article before the direct object the negative phrase is formed with kein/e/er. If there is no article in the affirmative phrase, the negative phrase is formed with keiner as well if there is no article and no other word between the verb and the object.

Note! I buy the book. Ich kaufe das Buch.   I don't buy the book.   He drinks coffee. Er trinkt einen Kaffee.   He doesn't drink coffee.   He drinks milk. Er trinkt Milch.   He doesn't drink milk.   He drinks a lot of milk. Er trinkt viel Milch.   He doesn't drink a lot of milk.   We buy a car. Wir kaufen das Auto.   We don't buy a car.   We see him. Wir sehen ihn.   We don't see him.   We see a man. Wir sehen einen Mann.   We don't see a man.   They listen to music. Sie hören Musik.   They don't listen to music.   They hear him. Sie hören ihn.   They don't hear him.   They give him money. Sie geben ihm Geld.   They don't give him money.   They give him the money. Sie geben ihm das Geld.     They don't give him the money.   He works. Er arbeitet.   He doesn't work.   He works a lot. Er arbeitet viel.   He doesn't work a lot.   He reads many books. Er liest viele Bücher.   He doesn't read many books.   I read other books. Ich lese andere Bücher.   I don't read other books.   He has the information. Er hat die Informationen.   He doesn't have the information.   He smokes only cigars. Er raucht nur Zigarren.   He does not only smoke cigars.   He drinks a lot. Er trinkt viel.   He doesn't drink a lot.   Sometimes he reads a book. Manchmal liest er ein Buch.   Sometimes he doesn't read a book.   They give a house to us. Sie schenken uns ein Haus.   They don't give a house to us.

Exercise 2: negation of einige - how would you do it? He reads some books. Er liest einige Bücher.   He doesn't read books.   Some books he doesn't read.

As you can see there are two possibilities depending on what you want to say. Doesn't he read any books? Ok, then it is Er liest keine Bücher. Or, does he just not like to read some books. Then it is: Er liest einige Bücher nicht.