I have gathered this list from multiple sources, and I have read all of these books. So this is my personal opinion.
1. Inspired: How to create (tech) products that customers love
by Marty Cagan
THE product management book to read. A new edition is more focused on tech companies and tech products, but it could be useful for any product manager. Provides a high-level overview of industry practices, skills, and the necessary changes in company culture.
Could be a bit biased at times, but it does offer a great deal of information.
2. User Story Mapping
by Jeff Patton
Presents a simple tool (user story map) that could be used to understand the desired product, and to ensure that the team is pursuing the right goals. While the concept is simple, the book goes into details of its implementation and provides best practices. A big part of the book contains specific cases, and I feel that they could be more relevant, or more precise. But it is an excellent book to read if you want to know how to write better user stories, and how to select and prioritize which features and user stories to develop.
3. The Product Manager’s Survival Guide
by Steven Haines
Helps to understand whether you would make a good product manager. Also provides development guidelines and tips on how to do your job better. The book assumes that the management often doesn't know what the product management is, and why are we trying to do it (as it is usually the case).
4. Measure What Matters
by John Doerr
Provides an overview of Objectives and Key Results. A powerful concept that allows companies to set strategic goals, and to ensure that all employees understand how they are contributing to the company. The idea was created and defined by Andy Grove at Intel (and he has described it in his book, "High Output Management"). John Doerr has further enhanced and elaborated that idea and provided some examples from different industries. Some people may find these examples too general, or not relevant enough, but I liked them.
5. The Phoenix Project
by Gene Kim, Kevin Behr, and George Spafford.
Easy reading on how DevOps culture and rapid experimentation could result in better products. A half-fictional book, but some details are very relevant for Product Management jobs. Takes a simple idea of a failing huge initiative, and how business focus could help technology teams to perform better. It stroke a chord for me, as I have been through a few IT transformations.
6. Power: Why Some People Have It—and Others Don't
by Jeffrey Pfeffer
This book is a collection of ideas and principles on how to influence people. In most of the cases, product managers have no direct authority and have to explain to their teammates why their role is essential. This book could provide a guide and general ideas on how to gain that influence, and how to rise in the organizational culture. Even though some of the listed methods are somewhat dubious, or too political, this could be a good read.