Grimoire etymologically is a word that indicates "manuals" for invoking Demons (or in general, how to contact Them), or, in a very general sense a book about Magick, Spells and Rituals. It's usually used in the first sense.
That being said...I made some research and apparently the grand grimoire, the red grimoire (also known as "Red Dragon grimoire") all refer to a work of uncertain datation (some say it dates back to the 1500s, some say it dates back to 1700s) of unknown authorship.
Apparently there was an older grimoire from which the red dragon grimoire was made from (and the latter is considered a counterfeit of the original) but the substance is the same: it's Solomonic magick. That alone should dissuade you from approaching those texts, if you know who Solomon allegedly is.
Solomonic magick grimoires like that one work under Judeo-Christian premises about the Gods: They are seen as malevolent Entities that are extremely violent and out of control and should only be contacted inside a "magickal protective circle". Not only that, the whole Great Work of the Evolution of Humanity of the Gods is kept outside the picture, and the Gods are approached for "deals with the devil" or in general for materialistic or otherwise opportunistic pursuits, basically using Them. That is very misguided and disrespectful towards Them, disregarding why They are there for us and Their Benevolence towards us and our advancement...
...and most importantly, those grimoires tend to work under the premise that the Gods are inferior to the christian god and therefore the magickian can "bid Them to do their will" and bind and subjugate Them.
That's magickal practice that is deeply rooted in jewish tradition and biblical narrative that is denigratory towards the Gods and implicitly connects you to biblical slanders. There is no reason to approach those grimoires.
Goetic is a word that is usually associated to Solomonic magick (like the Ars Goetia, part of the Lesser Key of Salomon, a grimoire) and interestingly is a word that indicates lesser magick, opposed to Theurgy. But that comes from the Wikipedia page, so I don't know. Goetic is usually a word you see with Solomonic magick, so be careful, though, it probably has other origins, probably from Ancient Greece (what I said before).
I don't know what Aurorae is, the 13th path either. 13 is a sacred Number I think, but I don't know what that path is.
If you have curiosities or crave for knowledge, ask the Gods for help. You will receive clear answers. I hope this is helpful though.