Entropy in classical thermodynamics is presented in a mysterious way that leads to confusion.
Entropy in statistical thermodynamics, however, is logical. Once one understands basic statistical thermodynamics, entropy isn't mysterious.
The book in my statistical thermodynamics class was An Introduction to Thermal Physics by Daniel Schroeder, which is an excellent book that I've referred to many times since.
The first time you study entropy, you won't understand it. The second time you study it, you'll think you understood it until you realize you didn't. By the third time you study it, you just don't care anymore and just use it.
To me, the issue with entropy is that it's initially presented without clear justification, so people don't know why it's important. Statistical mechanics made it clear to me that the state with the most entropy is the most likely to occur in equilibrium. (Statements about entropy representing "disorder" and whatnot in my opinion are handwavy, often lead to confusion, and should be avoided.)
Edit: but that was only after I had grokked Shannon's paper on information theory, which I felt was pretty intuitive.