Turning uniform draws into normal draws

What methods can you use to generate standard normal random variables starting from uniform random numbers?

Inverse transform, Box-Muller, Marsaglia's polar method or rejection sampling. Inverse transform sets $Z=\Phi^{-1}(U)$ using an accurate rational approximation. Box-Muller maps two uniforms to $\sqrt{-2\ln U_1}\cos(2\pi U_2)$ and the matching sine term, two independent normals. The polar method avoids trig by rejecting points outside the unit disc (acceptance $\pi/4$); rejection from e.g. an exponential envelope also works.