An Introduction to Conway's Games and Numbers
arXiv:math/0410026
Abstract
This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD of numbers, (4) ordinal numbers, (5) games and numbers, (6) infinitesimal games, (7) impartial games.
30 pages. Update 30 Sept 2005 containing some clarifications etc after acceptance for publication