Space Filling Curves The subject of space filling curves has generated a great deal of interest in the 100 years since the first such curve was discovered by Peano. Cantor Hilbert Moore Knopp Lebesgue and Polya are among the prominent mathematicians who have contributed to the field. However there have been no comprehensive treatments of the subject since Siepinskys in 1912. Cantor showed in 1878 that the number of points on an interval is the same as the number of points in a square (or cube or whatever) and in 1890 Peano showed that there is indeed a continuous curve that continuously maps all points of a line onto all points of a square though the curve exists only as a limit of very convoluted curves. This book discusses generalizations of Peanos solution and the properties that such curves must possess and discusses fractals in this context. The only prerequisite is a knowledge of advanced calculus