A synonym for “run through” is “peruse.” It means to read or examine something quickly or superficially. For example, you might run through a newspaper article to get the gist of it, or you might run through a book to see if it’s something you want to read.
Running through something can be helpful for getting a quick overview or for refreshing your memory. However, it’s important to note that running through something is not the same as reading it carefully or studying it in depth. If you need to understand something thoroughly, you’ll need to take the time to read it carefully and think about it.