Lecture Course III:
The theory of p-adic numbers, developed at the end of the 19th Century, is fundamental in modern number theory. It is based on an alternative definition of absolute value, which derives from a hierarchical (as opposed to sequential) arrangement of the integers. This device opens the study of integer congruences to the methods of analysis, and results in a number system with rather unusual properties. Recently, p-adic numbers have shown up in other areas of mathematics; this course is an introduction to the lively research area of p-adic dynamical systems.