Here are the authors whose writing I've found most helpful and influential when thinking about how to improve as an engineering manager.
High Output Management, by Andy Grove. My number one recommendation for anyone interested in managing people, particularly engineers. This book presents methods and processes for managing individuals, while remaining grounded in reality and humanity.
Thanks for the Feedback, by Douglas Stone and Sheila Heen. This book gave me great insight into how I handle feedback and what I can do to make the most of it. It also helped me understand how others might take my feedback, and develop methods for sharing my feedback effectively.
The Manager's Path, by Camille Fournier. A pragmatic guide to the stages of technical leadership, from tech lead to CTO. A great read even for engineers with no interest in people management, because it provides a clear line-of-sight into what those folks care about and how they make decisions.