This course is about analysis of functions in a complex variable. Topics include holomorphic functions, line integrals in the complex plane, Cauchy integral formula, isolated singularities, Taylor series and Laurent series, residues, conformal mappings, Weierstrass factorization, and the Riemann Zeta function. Applications of these ideas will lead to a broader and deeper understanding about topics in secondary school mathematics, including plane geometry, roots of polynomials, trigonometry, evaluation of series and integrals, and the study of prime numbers.