The following books are in my library on logistic regression analysis.
Applied Logistic Regression (Wiley Series in Probability and Statistics) This is the reference that I find myself going to the most. The book is comprehensive and readable. The mathematical level is not too high (although significantly higher than the level of this web site). The book does not use very much calculus, so if you are facile with math through collegelevel precalculus algebra, you ought to do OK with this book. But the word “facile” is very important in this last sentence. You will need to be comfortable with conditional probability, summation notation, product notation and the like. Basically, this book would be suitable for an undergraduate course in logistic regression. It is written for a different audience than the target audience of this web site — one that is a little more advanced. If you are serious about logistic regression, this book belongs in your library. I think this book is slightly denser that the book by Menard below and the two books differ in the special/advanced topics that are covered in the last few chapters of the book. If your interest is specific advanced topics, you should take a close look at the table of contents on Amazon. 

Logistic Regression: From Introductory to Advanced Concepts and Applications This is another very good textbook on logistic regression. It has slightly broader coverage than the book above by Hosmer et al. above. Similar level of mathematical ability is required. I think that this book would be an equally good choice as Hosmer et al. to be your key logistic regression reference. This book has slightly different coverage for the advanced/special topics from the ones covered in Hosmer et al., so you should take a look at the table of contents on Logistic Regression: From Amazon if the advanced topic coverage is important to you. 

Logistic Regression: A Primer (Quantitative Applications in the Social Sciences) INEXPENSIVE!!! This book is a primer in that it only covers the basic topics of logistic regression. But it is a nice little book and very inexpensive. I have put it near the top of my list not because I use it myself (I have the other two), but because if all you want is a basic reference, this book may well meet your needs. The math level required to understand this book is lower than the books by Hosmer et al. and Menard. There is less notation using conditional probability and summation and product notation in this book (although there is some). 