Mathematics Textbooks: Library Subscription and Open Access

2021 by Sheldon Axler, San Francisco State University.
Provide students with a deep understanding of the definitions, examples, theorems, and proofs related to measure, integration, and real analysis. The content and level of this book fit well with the first-year graduate course on these topics at most universities.

2004 by Elias Zakon, University of Toronto.
Leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Over 500 exercises (many with hints) assist students through the material.
Begins with set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces.

2013 by Richard Hammack, Virginia Commonwealth University.
The primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. How do we know a theorem is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm.

2015 by Bob A Dumas, University of Washington, John E McCarthy, Washington University in St Louis.
Intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course,