$$
\newcommand{\RR}{\mathbb{R}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\NN}{\mathbb{N}}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\FF}{\mathbb{F}}
% ALTERNATE VERSIONS
% \newcommand{\uppersum}[1]{{\textstyle\sum^+_{#1}}}
% \newcommand{\lowersum}[1]{{\textstyle\sum^-_{#1}}}
% \newcommand{\upperint}[1]{{\textstyle\smallint^+_{#1}}}
% \newcommand{\lowerint}[1]{{\textstyle\smallint^-_{#1}}}
% \newcommand{\rsum}[1]{{\textstyle\sum_{#1}}}
\newcommand{\uppersum}[1]{U_{#1}}
\newcommand{\lowersum}[1]{L_{#1}}
\newcommand{\upperint}[1]{U_{#1}}
\newcommand{\lowerint}[1]{L_{#1}}
\newcommand{\rsum}[1]{{\textstyle\sum_{#1}}}
\newcommand{\partitions}[1]{\mathcal{P}_{#1}}
\newcommand{\sampleset}[1]{\mathcal{S}_{#1}}
\newcommand{\erf}{\operatorname{erf}}
$$
Preface
This is the beginnings of a textbook for a course on real analysis. In its current form, it covers a bit more than 1-semester’s worth of material (with optional, skippable topics starred).