It is styled after a frequently-used device: "Alice in X", where X can be any kind of space which you wish to explain to the gentle reader. In this instance, Alice, along with Lewis Carroll and a Doctor WhatIf, gets to explore X=hyperbolic geometries. Poincare's disk is explained in great detail, along with lots of examples and exercises. Characters from "Wonderland" and "Looking Glass" make appearances at various places. Not a book you can read as a novel but fiction is fused completely with the mathematics (except for chapter-end problems). And the author does not waste much time diving into deep geometry so it is not an easy read. Uses a lot of puns, as is to be expected, some good and some groan-worthy. She's thrown in a few poems / limericks / doggerels as well along the way. The foreword to the book compares it directly to Synge's "Kandelman's Krim". The book is an enormous amount of fun if you like geometry. Heartily recommend it to anyone who loves mathematical toys in the abstract (though nothing abstract about geometry on a sphere or on a horse's back...)