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I am preparing a course on Nonlinear Analysis, and I need to teach the most important facts about Sobolev spaces to my students. I know most books on this subject, from Brezis' to Adams', from Mazya's to Leoni's. But I wonder if there you know a very short introduction, a chapter or a little book that you would define delightful for a beginner. Of course I do not need advanced topics: just the basics, the embeddings and the most important inequalities.

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Maybe Chapters 5 and 6 of Zimmer's Essential Results of Functional Analysis is what you're looking for. It contains an elegant introduction to the basics on roughly 50 (small) pages.

Here's the table of contents:

Table of contents

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