Reddit reviews An Introduction to Philosophical Analysis (4th Edition)
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Philosophical Problems and Arguments: An Introduction
James W. Cornman , Keith Lehrer , George Sotiros Pappas [Amazon Link] although published in 1991 it is going to leave out developments in the last 20 years.
But it does fairly well to present a rigorous exploration of 5 key issues in philosophy: God; Epistemology; Ethics; Free Will; Consciousness. Plus it has an overview chapter on Philosophy and its methods.
What makes it of particular interest is that the authors commit to defending particular answers in these areas after having traversed (as best they can) the main relevant issues and positions.
That confers an important understanding of philosophy: that is about trying to find answers to fundamental questions. Rather, as many folk regard philosophy, as a pointless exchange of views without any hope of progress.
Even some philosophers have an unfortunate antipathy toward answers in philosophy. I've heard one philosopher declare something like "Philosophy isn't about answers. If answers are provided in philosophy it becomes ideology and dogma. Philosophy is about questions."
Note the Cornman, Lehrer, and Pappas book can be a bit turgid in its writing style. So I'm glad you have a book of Russell's, Russell being a model of clear and plain expression. I haven't read his Problems of philosophy. I just might have to get it myself.
A friend also recommends An Introduction to Philosophical Analysis (4th Edition, 1996), John Hospers [Amazon Link].