This page is meant to be a respectful homage to (rather than a brazen rip-off of) Stephen Coles' fantastic and beautiful book The Geometry of Type (published as The Anatomy of Type in the US). It presents a selection of free web fonts in a similar style to the book. Hopefully it's a useful supplement to the book and a good encouragement for you to go out and buy a copy if you haven't already — seriously, it's not even expensive and is the best coffee-table book you could possibly wish for.
Fonts are grouped by the classifications used in the book. I have selected fonts that I like personally, are popular, are resonable stand-ins for fonts from the book or otherwise seem useful or interesting (such as fonts that work well as body text or have a variety of styles and weights).
Disclaimer: I am not a typography expert just an interested amateur so glaring errors in classification and crappy type-setting are to be expected! As much as anything this page was a way for me to learn about the characteristics of type by trying to classify fonts I already knew and liked as well as find fonts that fit into particular classification groups. This page is a GitHub project so if you feel inclined to correct anything then please send me a pull request.
Other useful resources for exploring free web fonts include Beautiful Web Type & Better Google Web Fonts