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The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the problems in the field. The topics covered include exponentiation and generalized e-numbers.

Synopsis:

These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.

1. Introduction; 2. Definition and Fundamental Existence Theorem; 3. The Basic Operations; 4. Real Numbers and Ordinals; 5. Normal Form; 6. Lengths and Subsystems which are Sets; 7. Sums as Subshuffles, Unsolved Problems; 8. Number Theory; 9. Generalized Epsilon Numbers; 10. Exponentiation; Index.

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