The theory of superconductors is an amazingly complicated and rich field, and it can be very daunting to begin studying without a large background in physics. This book does an excellent job telling you the details enough to understand what is going on without giving you so much that it becomes a daunting task to read the book.
Having only read through the first three chapters so far, I give that caveat before continuing.
The first chapter, the author says upfront, is difficult to follow, as it gives a quick outline of every future chapter in the book. I would recommend skimming the first chapter, and then after reading each chapter go back and see if you got the key points illustrated in the first chapter.
The second chapter, a treatment of the London equations, does an excellent job deriving the London equations in the first section, then providing a great deal of application of the equations, as well as outlining the limits of that model of superconductors.
Chapter 3 is where the book gets down to business, as Tinkham gives an introduction to BCS theory. This treatment uses plausibility arguements to justify many of the conclusions or assumptions, but also provides some guidance to the mathematical rigor you might use to really prove the assertions you make. The chapter does not leave you feeling very confused at all, and the section can be read almost straight through.
Although I have not read any further into the book, I can only imagine that it is more of the same. I would strongly recommend this book to anybody interested in learning something about superconductors before trying something more rigorous, such as Schrieffer's classic text on the work.