This seminal, multidisciplinary book shows how mathematics can be used to study DNA's first principles. Its most important contribution is to enrich the so called "Chargaff's grammar of biology" by providing the conceptual theoretical framework necessary to generalize Chargaff's rules. It begins with a simple example of DNA mathematical modeling where human nucleotide frequencies were associated to the Fibonacci sequence and the Golden Ratio through an optimization problem. However, its breakthrough was to show that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes when organized into a matrix form reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.