I didn't ask for any present this year because I didn't have any idea what I wanted.

However, I got somea present.

The first present I got iwas a book.

use past tense

It's called "The problem of Three-Body" (I am not sure about the name).

The Three Body Problem.
I know that book

My older cousin read it and saitold me that it's really cool.

However, he read it in French and it was already difficult for him so I think it won't be easy for me to read it.

It also has a séeries on Netflix .

Another problem that makes the book more difficult to read is that it' was originally written in Chineese and the character's' names aren't easy to memorize and associate.

I started reading the first book 1 month ago, and I am currently at the page 360.

I think reading those books will definitely help me forwith reading the book I got for Christmas.

Please tell me howwhat you foundthought of my English!

This Christmas, it was weird.

I didn't ask for any presents this year because I didn't have any idea what I wanted.

It sounds a bit more natural adding “what I wanted” to clarify what idea you mean.

However, I got some presents anyway.

“anyway” is needed to reinforce that this happened in spite of what you said previously.

The first present I got iwas a book.

Tense should be consistent throughout

My parents offered it to me in English, so I can improve my writreading comprehension.

My older cousin read it and saitold me that it's really cool.

Another problem that make the book more difficult to read is that it' Chineese and the character's’ names aren't easy to memorize and associate.

A Plural possessive like “characters” gets an apostrophe after the s, not before

I started reading the first book 1 month ago, and I am currently at the page 360.

My parents offered itgave it to me in English so I can improve my writing and comprehension.

My older cousin has already read it and saitold me that it's really cool.

However, he read it in French and it was already difficult for him so I think it won't be easy for me to read it.

It also has a séeries on Netflix .

Another problem that make the book more difficult to read is that it's Chineese and the character's names aren't easy to memorize and associate.

Before I read this book, I haved to read the entire series of Divergent.

Please tell me how you found my English!

It’s good, keep it up :)

This Christmas, it was weird.

You don't need to use "it" to refer back to "this Christmas" when you just mentioned "this Christmas", better to keep it simple.

I didn't ask for any present this year because I didn't have any idea.

"ask for X [from Y]" -> requested someone to give you X
"ask X" -> requested something of person X

(Note there are exceptions here, you can "ask a question [to someone]" or "ask a favour [of someone]", but present is not one of those exceptions)

However, I got some presents.

Since there's more than one, it should be "presents" instead of "present"

The first present I got iwas a book.

"was" to match the tense of "got"

It's called "The problem of Three-Body" (I am not sure about the name).Three-Body Problem"

The English name of this book is "The Three-Body Problem"

My older cousin read it and (said meto me / told me) that it's really cool.

"said" assumes the next thing is the topic that was said. "told" on the other hand assumes the next thing is the recipient. You can use "say to" or "tell" here, but "tell" is more natural. ("told" since it's past tense)

It also has a séeries on Netflix .

English rarely uses diacritics and series isn't a word that they used for.

Sometimes in very formal writing you'll see café or naïve, but even for those words the diacritics are optional and usually omitted in standard writing (particularly because people don't actually know how to type them)

Another problem that make the book more difficult to read is that it's Chineese and the character's names aren't easy to memorize and associate with the characters.

"associate" needs more information.

I started reading the first book 1 month ago, and I am currently at the page 360.

I think reading those books will definitely help me forwith reading the book I got for Christmas.

This Christmas, it was weird.

I didn't ask for any present this year because I didn't have any ideaknow what I wanted.

However, I got some presents.

It's called "The problem of Three-Body Problem" (I am not sure about the name).

I think this is the book you're talking about. I know that title.

My parents offered itgave it to me in English so that I can improve my writreading comprehension.

I assume you meant reading comprehension since you'll be reading this book.

My older cousin read it and saitold me that it's really cool.

However, he read it in French and it was already difficult for him so I think it won'might not be easy for me to read it.

It's a science -fiction book about a physics problem.

We hyphenate this term. Alternatively, you could say "sci-fi" - shorthand for science-fiction.

It was also hasmade into a séeries on Netflix .

Another problem that makes the book more difficult to read is that it's Chineese and the character's names aren't easy to memorize and associate.

Before I read this book, I have to read the entire series of Divergent series.

A bit more natural.

I started reading the first book 1a month ago, and I am currently at theon page 360.

I think reading those books will definitely help prepare me for reading the book I got for Christmas.