Random analytic functions have been attracting the attention of mathematicians since the 1930s, though the focus of interest has been changing with time. Just as the distribution of eigenvalues is the essence of the random matrix theory, central to the study of random analytic functions are their zero sets.

Since the late 1990s, the subject was revived by several groups of researchers. They established new links to complex and harmonic analysis, mathematical physics, probability theory and geometry, which drastically changed the whole subject.

In this short course, I plan to introduce the audience to this subject.

I will try to present a glimpse of some of recent discoveries and questions, which remain open.