I started reading recently, and I found an interesting book at the library called Descartes's notebook.

I would combine these two clauses together.

And I found an interesting book at the library, Descartes's notebook.

I put this one above with the first.

It's about the creator of the cCartesian plane and the analytical geometry.

The author starts the book withby presenting how one of the greatest mathematicians obtained some samples from Descartes's notebook.

After that, the notebook disappeared forever.

Then the author starts with Descartes's biography, talking about his childhood and how he started to learn about science at Ludving IV's castle that was given to the church.

After Descartes had finished his studies, he will started looking for knowledge and adventure.

For that, he will join voluntaryjoined the army, and will assists a volunteer and served in different battles.

This period had also played a big part in his development as he founded new friendships with differenet famous mathematicians and phiysicians.

His love for science did amplifygrew in this period, and he developed a new knowledge about philosophy, mathematics and pishhysics.

He had strange dreams about life that made him think it's a sign for himhe understood as a sign.

Trying to express his knowledge through books was an empty idea because the cCatholic cChurch was destroying everything that was wrong from their perspective or "God's will".

It's about the creator of the cartesian plan and the analytical geometry.

There is no article when talking about a subject matter: I study geometry, I like psychology etc.

The author starts the book withby presenting how one of the greatest mathematicians obtained some samples from Descartes's notebook.

Then the autor starts with Descartes's biography, about his childhood, and how he sarted to learn about science at Ludving IV's castle that was given to the church.

After Descartes had finished his studies, he will started looking for knowledge and adventure.

After X, he will start Y. Gives the impression that he has not started Y yet.

ForTo that he will join voluntaryend, he joined the army, and wills a volunteer and assisted different battles.

This period had also played a big part in his development as he founded new friendships with diferenet famous mathematicians and phiysicians.

His love for science did amplify in this period, he developed a new knowledge about philosophy, mathematics and pishhysics.

Trying to express his knowledge through books was an empty useless idea because the catholic church was destroying everything that was wrong from their perspective or against "God's will".

And I found an interesting book at the library, Descartes's notebook.

There's not really a need for and here but you could also have just make this one sentence or gone with "And, I..."

is the title Descartes Notebook?

It's about the creator of the cCartesian pPlane and the aAnalytical gGeometry.

I believe these are proper nouns. Cartesian is even if Cartesian Plane isn't.

The author starts the book with presenting how one of the greatest mathmatican obtained some samples from Descartes's notebook.

After that the notebook disapeared forever.

This is a little weird because the sentence before is about how the author started the book not about the history. You may have need a single longer sentence, unfortunately.

Then the autor startproceeds with Descartes's biography, about; discussing his childhood and how he started to learn about science at Ludving IV's castle that was given to the church.

you are using "starts with" repetitively, I'm not sure what the second half of this sentence means but it is definitely needing to be rewritten so I just removed the confusing parts.

After Descartes had finished his studies, he will startbegan looking for knowledge and adventure.

will is future tense here which is baffling.

For that he will join voluntaryjoined the army, and will assisted in different battles.

assisted is a strange way to say participates but I'm not sure if you have a different idea here.

This period had also played a big part in his development as he founded new friendships with differenet famous mathematicians and phiysicians.sts

physicians or physicists?

His love for science did amplifyied in this period, he developed a new knowledge about philosophy, mathematics and pishhysics.

spell check will save you from many corrections!

Trying to express his knowledge through books was an empty idea because the cCatholic cChurch was destroying everything that was wrong from their perspective or "God's will".

I'm not familiar enough with the context to 100% understand this unfortunately