This introductory text is designed to entice non-math focused individuals into learning some mathematics, while teaching them to think mathematically. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results. Pythagorean Triples, Linear Equations and the Greatest Common Divisor, Factorization and the Fundamental Theorem of Arithmetic, Congruences, Mersenne Primes, Squares Modulo "p," Quadratic Reciprocity, Pell's Equation, Diophantine Approximation, Irrational Numbers and Transcendental Numbers, Sums of Powers, Binomial Coefficients and Pascal's Triangle, Elliptic Curves and Fermat's Last Theorem. For individuals with limited math experience who are interested in number theory.