This book is called ‘21 lessons for the 21st century’.

Thise book is written by Yuval Noah Harari.

This author also wrote two other books and they are really good.

This works, but you could also say "This author has also written two other books and they are both really good."

You can learn a lot of information from this book.

It's assumed if you're learning from a book that you are learning it's information, so no need to add it in this case.

This book writetalks about the enviroment, history, education, technology,.... A and 21 lessons will teach yabout what you need to learnknow if you want to survive in this century.

People write - books have words and 'talk' to you!

This book is ‘21 lLessons for the 21st century’.

This book write about environment, history, education, technology,.... Aand '21 lLessons' will teach you what you need to learn if you want to survive in this century.

This bookIt is written by Yuval Noah Harari.

Grammatically your sentence is fine, but it sounds more natural to use pronouns (eg he/she/they/it) after the first time you talk about something.

This author also wrote two other books and they are really good books.

Again, grammatically your sentence is correct, but could be improved to sound more natural by using one sentence instead of two,

This book writeis about the environment, history, education, technology,.... And '21 lessons' will teach you what you need to learn if you want to survive in this century.

Fixed a minor spelling error in "environment".

Not sure what you mean in the last part. I corrected it as if you meant: The book will teach you what you need to learn.

But you could also mean: This book is about the environment, history, education, technology,.... and 21 lessons you need to learn if you want to survive in this century.

Which is saying This book is about these things, and the 21 lessons.