
I have all of his books and they are all great (though not easy!). His starting point is "Algebraic Structures" (basically sets of objects and operations defined on them eg. Groupoid/SemiGroup/Monoid/Group etc.) and so some familiarity with Abstract Algebra/Discrete Mathematics is assumed. The mapping he does from the mathematics to a language construct modeling a concept is what gives one the insight into programming. His other book From Mathematics to Generic Programming gives one a more "easier" approach to the subject and should be read in conjunction with this one for better understanding.
A related old book is Ruminations on C++: A Decade of Programming Insight and Experience by Andrew Koenig and Barbara Moo. This is derived from a collection of articles written by Koenig when he was working closely with Stepanov on his ideas and implementation of STL. His idea of programming templates in a functional and generic manner is what is conveyed in this book in the "templates" section and is still quite illuminating (no math but short C++ code in articles). So something which might not be clear from Stepanov's mathematical treatment may be clearer here since you can see an actual C++ implementation (warts and all).
I was lucky that i discovered C++ early and hence started with it as a "better C". I was not exposed to a lot of upfront complexity (eg. template shenanigans) thus making my learning curve easier. The big mistake people new to C++ make is trying to learn all language features and dark corners. Instead you should look at various aspects of the language separately and understand their applications. That way you learn how to model the problem domain using the appropriate syntactic features of the language. Here are a few different ways of looking at and using the language.
1) As a better C - You can define stricter types, control memory management using techniques like RAII/Smart pointers and enforce better modularization.
2) As an Object-Oriented language - Here you design class hierarchies and provide interfaces, domain libraries and frameworks.
3) As a Generic programming language - Here you define types and learn how to combine them using composition and delegation.
It might be helpful for you to read some of the older C++ books (Modern C++ IMO is more complicated since it mixes the language features in a free manner) to get at the root of "how to think in C++". To that end you might find the following useful;
1) Ruminations on C++ : A Decade of Programming Insight and Experience by Andrew Koenig and Barbara Moo - short chapters explaining various implementation techniques in C++.
2) Scientific and Engineering C++ : An Introduction with Advanced Techniques and Examples by Barton and Nackman - This book will teach you how to design in C++
3) Multi-paradigm design for C++ by James Coplien - Advanced book teaching you how to map problem domain concepts onto language features.
IMO, If you grasp the gist in the above books, you will understand "the heart of C++" and can easily pick up "Modern C++".