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Surfaces And Essences, by Douglas Hofstadter and Emmanuel Sander, is the only book I can think of that's explicitly about analogies.  But there's no reason to feel uncomfortable, since in both look and content--or surface and essence--it's a lot like previous Hofstadter books about how we think*. And that's the point.  Analogies aren't just things that come to us occasionally, they're, as the book has it, the core of cognition.  From childhood, we're faced with novel or at least ill-defined situations, and we're not dumbfounded, because we compare them to what's happened before. We experience the world through analogical thinking.

Hofstadter builds his argument slowly, always offering plenty of illustrations, starting with how evocative words and phrases can be.  By the end he's discussing analogical thinking that changed the world, such as Einstein's. 

I don't want to diminish Sander's contribution.  This reads like a Hofstadter book, but no doubt the collaboration of this French colleague was essential.  In fact, the two published a French edition of the book to coincide with the English version.  Parts of the book explain how it wasn't just a translation, but deep work in analogy: how do you "translate" a paragraph about the everyday experience of traveling on Le Metro in ways that Americans can appreciate.  It's about more than words, it's about deep experience with the world.

I don't know if this book will be as popular or influential as previous stuff from Hofstadter, but it's certainly a worthy continuation of his work.

*Now that I think of it, I have read a book about analogies before--Hofstadter's Fluid Concepts And Creative Analogies.