I still think the exposition on elliptic functions in Jacobi's Fundamenta Nova (1829) is one of the best I've encountered if you are interested in the functional relationships. A close second for me is Cayley's An elementary treatise on elliptic functions (1895), especially for the number of alternative proofs presented and the numerous relationships detailed. Modern books tend to take the algebraic approach, which is obviously extremely important for understanding the true nature of the relationships here, but for those of us who study the field because of it's incidental use in combinatorics and generating functions, these older books are a wealth.
Also, I have a personal love of Gauss' Disquisitiones Arithmeticae (1798) because it introduced me to number theory at a young age in a way that was very natural and elegant. Again, I appreciated it's approach to forms and related because it was all easily understandable with middle school algebra.
And finally more modern, for me Goldblatt's Topoi: The categorial analysis of logic (1979) is the best introduction to categories one could have, far better in my opinion than even Mac Lane's. That it is also subversive propaganda for constructivism is also a huge bonus.