The aim of this book is to introduce people without a strong physics (or even scientific) background to the special and general theories of relativity - theories that Einstein was the primary developer of. Einstein assumes the reader has passed a "university matriculation exam." What that meant in the first half of the 20th Century, I don't know but in practice what's required is the level of algebra I had by age 16 plus a smattering of mentions of the square root of minus 1. I also found basic calculus useful for one section, though it is possible to do without it.
For the most part this book is excellent, introducing the minimal amount of mathematics and formal language necessary to understand the most important and fundamental concepts of Einstein's theories in a way that is accessible whilst concise. It might be possible to do it better with a bigger book, a less formal style and a lot more diagrams but it very interesting to get Einstein's unique perspective as originator of the theories and insight into his thought processes.
A few sections are remarkable in contrast with the rest, for being unclear. The section on addition of velocities in special relativity leaves rather more to the reader than anything else in the book, mathematically, and when I looked it up it turned out to be much easier to work out using basic calculus than algebraic division - and the bit that wasn't clear was that a division of two equations was what was required. This section could be skipped without losing much.
The remainder of the muddy sections come at the back end of the section on general relativity. The simplest precise mathematical formulation of this theory is expressed using tensors - and tensor algebra is way beyond what anybody encounters in standard school maths or physics curricula. Einstein makes no attempt to explain it and in fact never shows the fundamental equation of general relativity. This makes it very hard for him to explain how gravitational fields and space-time interact, which leads to the lack of clarity in the latter stages of this part of the book. Things get easier and clearer again when he moves on to relativity and cosmology.
The final part of the book is a collection of appendices expanding on things discussed earlier on. I required pen and paper to check the derivation of the Lorentz Transformations from first principles - but this section could just be skipped if the maths bothers you - it doesn't add a lot but it is interesting to see it, if your algebra is up to it.
The most rewarding thing for me, since nothing here is completely new to me, was listening to Einstein's voice. He seemed to come at things from a viewpoint much more generally philosophical than most present day physicists would, discussing Kant, Descartes and Hume, for instance. The section on the concept of "empty space" was fascinating - he concludes that general relativity precludes this notion - one cannot have space-time without it containing "fields." What he means is fields of force - the electromagnetic field, gravitational field etc. This implies the notion of a field being present even if its magnitude is zero - which is a bizarre concept. Modern quantum mechanics backs these ideas to the hilt and leads me to think that one of the most important areas of inquiry for fundamental physics as it stands is the connection between the classical idea of space-time and the quantum idea of the vacuum. The fundamental nature of both is obscure - and in some sense they should be the same thing.
Overall this is an excellent introduction to special relativity and at least the conceptual underpinnings of general relativity, if not of the full theory, which really just can't be explained properly without knowledge of tensors.