$$
\newcommand{\RR}{\mathbb{R}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\NN}{\mathbb{N}}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\EE}{\mathbb{E}}
\newcommand{\HH}{\mathbb{H}}
\renewcommand{\SS}{\mathbb{S}}
\newcommand{\DD}{\mathbb{D}}
\newcommand{\pp}{^{\prime\prime}}
\newcommand{\p}{^\prime}
\newcommand{\proj}{\operatorname{proj}}
\newcommand{\area}{\operatorname{area}}
\newcommand{\len}{\operatorname{length}}
\newcommand{\acc}{\operatorname{acc}}
\newcommand{\ang}{\sphericalangle}
\newcommand{\map}{\mathrm{map}}
\newcommand{\SO}{\operatorname{SO}}
\newcommand{\dist}{\operatorname{dist}}
\newcommand{\length}{\operatorname{length}}
\newcommand{\uppersum}[1]{{\textstyle\sum^+_{#1}}}
\newcommand{\lowersum}[1]{{\textstyle\sum^-_{#1}}}
\newcommand{\upperint}[1]{{\textstyle\smallint^+_{#1}}}
\newcommand{\lowerint}[1]{{\textstyle\smallint^-_{#1}}}
\newcommand{\rsum}[1]{{\textstyle\sum_{#1}}}
\newcommand{\partitions}[1]{\mathcal{P}_{#1}}
\newcommand{\erf}{\operatorname{erf}}
\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}
\newcommand{\smat}[1]{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)}
$$
Dedication
This is the first draft of a future textbook in modern geometry at the advanced undergraduate level. It was used as the course text for the course Foundations of Geometry at USF in the Fall of \(2023\).
This very first edition is dedicated the students of that course: Alana, Daniel, Emelia, Frances, Katie & Quinn.
Thank you for your patience as I wrote these notes live over the course of the semester, and your enthusiasm which motivated me to continue writing each evening, even when I began to realize I committed to a much bigger project than I should have for the term.