Cremona groups and their subgroups (Dolgachev)

A Cremona transformation in dimension n is a birational automorphism of n-dimensional projective space, or, algebraically, an automorphism of the field of rational functions in n variables identical on the coefficients. The group Cr(n) of such transformations is named in honor of Luigi Cremona who initiated a systematic study of this group in the middle of the 19th century. In my introductory lectures I will survey classical results and modern developments using minimal background in algebraic geometry and concentrating more on concrete examples.