In my opinion, there is no single book that provides a balanced treatment of the conceptual and mathematical aspects of thermodynamics. Next, I indicate the books that have facilitated the understanding of this topic.
*Concepts
Four Laws That Drive the Universe , Peter W. Atkins, OUP, 2007
No special concepts of mathematics are needed
*General
Books of undergraduate physical chemistry such as Atkins o Silbey are my favourites. Also, I highly recommend McQuarrie's book: "Physical Chemistry: a molecular approach"; this books provides a clear link between classical thermodynamics and modern concepts of basic statistical thermodynamics (molecular basis of the thermodynamic's fenomena)
This books only require knowledge of single variable calculus and familiarity with the concept of partial derivative. If you want to learn this topics in physical chemistry context , I recommend this book:
The Chemistry Maths Book, Erich Steiner, OUP, 2008