The Loewner equation: Maps and shapes

An approach called Schramm-Loewner evolution (SLE) provides a new method for dealing with a wide variety of scale-invariant problems in two dimensions. This approach is based upon an older method called Loewner Evolution ( LE), which connects analytic and geometrical constructions in the complex plane. In this paper, the bases of LE and SLE are described and some simple applications are discussed in relatively non-technical form. A bibliography of the subject is presented.