Since I'm reading this book, I thought thait would be interesting to write a summary of each chapter.

"it" is a placeholder noun here, since you're saying "writing a summary would be interesting". You'd only use "that" if you were talking about something you've already mentioned. For example, "Would you like a summary of each chapter? I think that could be interesting."

So, tThe Writer's Journey is written by Christopher Vogler.

This isn't wrong, I'm moreso commenting on it, but in written/formal texts we usually omit any fillers like "So" unless they're used as a conjunction or something. The "so" would be fine if this was spoken, or if this was a review sent to one of your friends, so it's fine to keep.

The introduction explains how all of the stories, or at least most of them, share a common narrative structure made of specific elements.

"all stories" works but is less natural here, since you're talking about stories from a specific source. It would be fine if you were making a comment on every story, e.g. "All stories should have conflict in them".

Volger's advice is to learn this kind of narrative structure and to analyze, read, view multiple times a movie or a book that we like and read/watch a book/movie that you like multiple times to understand how everything unfolds.

"analyze, read, view" should fit with the nouns we give (books and movies), but you can't read movies (you generally watch movies instead of view them, though to view a movie isn't exactly incorrect) and you can't view books. It should instead be "analyze and read or view a book or movie" (maybe replace the "or"s with slashes for brevity and readability)
"multiple times" is a frequency and if you wanted to stress it you should make sure not to split the verb from it's object or the adverb of "that we like". The only good position in this case would be at the end.
This is more nitpicky, but sometimes you may want to clarify the last clause, "that we like to understand how everything unfolds". I assume it's meant to read "(analyse the media) that we like, so that we can understand how everything unfolds", but you could also initially read it as "we like to understand how everything unfolds". It's not necessarily, but you could put something after "we like" to show that you're talking about something else, e.g. "so that we can", "in order to".
You also used the second person "you" for in this summary to refer to the reader ("this is something you can find"), but in this paragraph you use "we". A lot of publications and text use "we" to refer to the author and the reader in order to sound more alike or to suggest that the author was in a similar place to you, and there's nothing wrong with that in this text, but you should be consistent across it.

The Writer's Journey, sSummary : Introduction

Since I'm reading this book, I thought that it would be interesting to write a summary of each chapter.

This would be a great opportunity for me to improve my writing skills.

So, tThe Writer's Journey iwas written by Christopher Vogler.

If the title is "The Writer's Journey" then the first "the" should be capitalised. Also, the book is written so "was" rather than "is".

These elements help structure the narrative throughout a story and can be labeled as "The Hero's Journey".

This is something you can find in all myths and legends, and it has been used in our modern stories as well.

Volger's advice is to learn this kind of narrative structure and to analyze, read, or view multiple times a movie or a book that we like tomultiple times so that we understand how everything unfolds.