How to Think about Analysis, Lara Alcock, Oxford University Press, Oxford, 2014

I have previously commented on Alcock's earlier work, How to study as a Mathematics Major.  This book is even better.  The first 50 or so pages are about learning analysis. The balance of the book reviews the central concepts of analysis unencumbered by the need to prove everything - which will, of course, be done in the actual course.  So what we have here are research-informed strategies for learning analysis.  I would recommend this to all students (Math, Physics, Chemistry, EE, etc.) who need to take advanced courses in mathematics.  It would also help faculty who are preparing mathematically oriented courses that make use of the material covered in rigorous calculus and real analysis classes.