Andrew D. Hwang<p>"An Invitation to Real Analysis" should be out in October. I hope the book helps students around the globe learn real analysis for many years into the future. In any event, getting to tell this story of numbers, sets, functions, sequences and limits, and function spaces is something I got to do in my time here on earth.</p><p>If you are teaching introductory real analysis in Winter/Spring 2026 or beyond, I am deeply grateful for your consideration. The book was written for courses covering material from basics of sets and proofs at one endpoint to metric spaces and selected applications in function spaces at the other. There are over 600 exercises at all levels of challenge. Selected hints, answers, and solutions are in the back, and a complete solution manual will be available for instructors.</p><p>Throughout, I've striven for readability, simplicity, networks of conceptual connections, and consistency of notation and terminology. Consistency was not as straightforward a goal as I first expected.</p><p>There are a few noteworthy choices--such as using descriptive terms in favor of eponyms, and counting starting from 0--that I believe are features even if at first they seem not to be. Other pedagogical choices include using adversarial games systematically to convey analytic definitions, acknowledging the "foreign language" aspects of analysis, and putting material in strict logical order to the extent possible so readers can easily tell at any stage what concepts and results are available for use.</p><p>I'll post further details, including the publisher's web page for the book, once I'm formally notified.</p><p><a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Math</span></a> <a href="https://mathstodon.xyz/tags/ITeachMath" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ITeachMath</span></a></p>