This work specifically surveys simple Noetherian rings. The authors present theorems on the structure of simple right Noetherian rings and, more generally, on simple rings containing a uniform right ideal U. The text is as elementary and self-contained as practicable, and the little background required in homological and categorical algebra is given in a short appendix. Full definitions are given and short, complete, elementary proofs are provided for such key theorems as the Morita theorem, the Correspondence theorem, the Wedderburn Artin theorem, the Goldie Lesieur Croisot theorem, and many others. Complex mathematical machinery has been eliminated wherever possible or its introduction into the text delayed as long as possible. (Even tensor products are not required until Chapter 3.)