How should the name of a series of books be formatted?
Since you're not using a style guide you can do whatever you want in terms of formatting. Or you can follow a style guide.
I think the following recommendation from the MLA website is pretty logical:
The question of how to style a trilogy or series of books or movies that has no official title is less clear. For example, would it be the Star Wars movies or the Star Wars movies? Your decision will depend on what makes sense for the particular body of work. Star Wars is the name of the first movie released in the series. Since the title is foundational, italicize the series name: Star Wars movies. If you are writing about the Nancy Drew books, style the series name roman, since "Nancy Drew" does not appear in the titles of the individual books. If you are discussing the Harry Potter books, you could style the series name either way—Harry Potter books or Harry Potter books—since the series is associated with the first title in the series (Harry Potter and the Sorcerer's Stone) and also with the character's name.
As others said above, if you're not following a style guide, use your own discretion. I wanted to add one more point of reference as well. According to Chicago style (link, link), book series titles generally are not italicized, but there are two exceptions:
- if the book series name is the same as the title of an individual book, or
- if there is a separate title for the entire series as a whole (for example, His Dark Materials).