Intended for advanced undergraduates and graduate students in mathematics, physics, and chemistry, this work teaches problem-solving using the theory of special functions. The concise treatment demonstrates the theory's use and application to a wide variety of problems in atomic and molecular physics. Topics include hypergeometric function and polynomials, discrete spectrum eigenfunctions, linear harmonic oscillators, Kratzer molecular potential, and rotational correction to the Morse formula. AUTHORS: Professor Bolotin and Professor Raudeliunas are retired from the faculty of Vilnius University in Lithuania.