I've noticed that most tv series have a short part, usually 1~2min, before the theme song comes in. Is there a particular name for that? Thanks!
You can call it a "cold open" or a teaser. According to Wikipedia,
A cold open (also called a teaser) in a television program or movie is the technique of jumping directly into a story at the beginning or opening of the show, before the title sequence or opening credits are shown. On television this is often done on the theory that involving the audience in the plot as soon as possible will reduce the likelihood of their switching away from a show during the opening commercial.