We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts to recent results, and allowing for a simple comparison-at-a-glance between different constructions.
"Survey Article: The real numbers–A survey of constructions." Rocky Mountain J. Math. 45 (3) 737 - 762, 2015. https://doi.org/10.1216/RMJ-2015-45-3-737