I am delighted to announce that my first book, Linear Fractional Transformations: An Illustrated Introduction, has now been published Springer’s Undergraduate Texts in Mathematics. You can find the product page here: Springer Product Page. It is available both as a hardback and e-book. If you are interested in the book but are unsure if you want to purchase it, an excerpt from the preprint of this book can be found here: LFT Chapter 2. (But do bear in mind that the finished product is of a significantly higher quality.)
Linear Fractional Transformations is aimed primarily at an undergraduate audience, such as first-year mathematics students who wish to see some beautiful mathematics beyond the calculus/linear algebra curriculum. It is lovingly illustrated: in the final ~250-page manuscript, there are over a hundred different figures (many of which are made of several individual drawings). There were, in fact, too many illustrations and too much material in the original preprint, and almost half of it had to be cut. I am confident, however, that this material will eventually make it into future books.