a question I have(I'm still new to lancer and I'm trying to host a game), can I just buy and play this with my group, or do I need to have the core book too?
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you can download the core book for free by going to massif press' main page https://massif-press.itch.io/.
Look for the free version, it contains the rules and other essentials, but doesn't include advice/guidance for the GM as well as some other non-essential details.