Space physics is a young discipline in Turkey. Since 1970 various national near-Earth space research activities and several international collaborations have been conducted in Turkey and some of these are continuing. In May 2004 a four-week Graduate Course on "Space and Atmospheric Physics I and II" was held at the Tubitak Feza Gursey Institute in Istanbul, Turkey. This paper explains the background behind this initiative, and gives an introduction to the topics that were covered during the course, especially emphasizing how solar-terrestrial physics is applied to space weather. During the course the students, in parallel with the lectures delivered, performed projects based on the curriculum, and using information available on the Internet and in the literature. A resume of their results concerning the well-known "space weather" event at the end of 2003 is given.