I've been a Product Manager for over a decade and in that time have read hundreds of books. These are the 3 at the top of my list for breaking into the field:
"Inspired" by Marty Cagan
This should be your first stop.
The classic book that has it all. Covers Product Management from cultural, strategic and tactical perspectives. It'll give you a sense of the industry and how PM's fit (or should fit) within orgs. It also has great concrete guidance on how to do the job.
If you read one book, this should be the one.
"Don't Make Me Think" by Steve Krug
If you don't want your products to suck. Read this.
The book is a little more focused on UX and Research, but that can be at the core of what a PM does. Make products that people want to use. The book is relatable and an easy fun read.
The last chapter on UX Research is also a gem, that he broke out into another classic, "Rocket Surgery Made Easy"
"The Product Manager's Survival Guide" by Steven Haines
Another solid intro to how to PM in an Org.
This book has a little more of a strategic and attitudinal approach. ie. How to actually exist and think as a PM in an org. Well worth the read as it'll set you up for success when working within an organization.
Honorable Mentions:
These are a little more process focused (scrum in particular) and will set you up with a solid tactical foundation for breaking work down (even if you don't use scrum, which I don't really anymore):