This "Introducing" series is alright. The Introducing Heidegger book was definitely a concise overview of his philosophy. Introducing Existentialism was more complex. Appignanesi discussed Husserl, Heidgger and Sartre in bits and pieces, stitching convergent threads of their philosophies to create "a nameless philosophy." His summary of the "unidentified convergence in [the] trio's antagonism" - he suggests "existential phenomenology" - in the last two pages is really what you should read first. Or maybe all you should read.
Read the book in one sitting. I read the first 50 pages 3 different times, and then started in the middle when I picked it up again, and I was a little lost. It's meant to be a one-day read. But it's worth a few hours.