* D E L E G A T E => Your job is to keep your people productive and effective. Doing that starts with yourself - do the things only YOU can do and delegate the rest to the people who are better served to handle that.
* Check out the Manager Tools podcast and focus on the basics (https://www.manager-tools.com/manager-tools-basics)
* The 2 books I got solid, actionable advice from were "The First 90 Days"  and "The 27 Challenges Managers Face" 
1. "Thinking Strategically," written by a professor at the Yale School of Management and an economics professor at Princeton.
This one is basically a primer on game theory, which I think would be useful for you particularly if you are facing off someone at work. It gets you thinking about incentives of each party and figuring out the different ways situations could play out.
2. "The First 90 Days," published by Harvard Business Review Press.
Obviously, it's targeted at those transitioning into a new leadership position, but in my opinion the strategies can apply even to those who are in incumbent positions as it's never too late to turn the page and start taking a fresh approach or step up one's level of effort at work.
It includes an actionable plan for feeling out the pain points of others you need to impress and tackling their problems in a visible manner. This one is less about politics per se but more about being a very effective leader in a highly visible manner, which can help one to move up the ladder.
Get dozens of book recommendations delivered straight to your inbox every Thursday.