The classical "theory of complex variable" is considered by some as one of the most beautiful and useful subjects in mathematics. This concise introduction is based on the premise that "anything worth doing is worth doing with interesting examples". Content is driven by techniques rather than by definitions and theorems. Examples are chosen from the analytic theory of numbers and classical special functions, but while they are mostly geared towards number theory, mathematical physics, the techniques are generally applicable. Prerequisites are a standard course in calculus.