Reddit mentions of Husserl’s Phenomenology (Cultural Memory in the Present)

Shaun Gallagher's Phenomenology is a great introduction, and covers a lot of the areas and distinctions made by philosophers.

Dan Zahavi's Husserl's Phenomenology is actually pretty decent. He considers other positions and how they relate to the O.G. of phenomenology. Plus, Zahavi is a freakishly clear writer.

Edit/PS: "Introductions to Heidegger" are often hard to recommend, but with your political philosophy bent, I'd suggest Irene McMullin's Time and the Shared World: Heidegger on Social Relations. I can't wholeheartedly recommend the book, as I have yet to read it, but reviews speak highly of it.

And, as far as I'm aware, Richard Polt's Heidegger: An Introduction is a core book in its comprehensive overview of Heidegger's works.

The phenomenological mind is pretty good, although its not a typical introduction, more like a summary of the main phenomenological topics, without going into detail of each phenomenological thinker, their main ideas, and comparing it across other phenomenologists. Zahavi also has a good introduction to Husserl.