Question: could anyone tell me what's the background theories in The Definition of Standard ML, found very interesting and beautiful, i did learn some sml a little, but i want more while don't know how to start (to understand TDSML)

3x in advance

Answer: 
For the old version of the Definition (SML'90) there actually was a separate book called "Commentary on Standard ML", which explained how to interpret the Definition. Both the SML'90 Definition and the Commentary are long out of print, but fortunately, are available as [free PDFs](http://www.itu.dk/people/tofte/publ/1990sml/1990sml.html).

The SML'90 Definition had some differences to SML'97, in particular regarding the module system. Overall, it was more complicated. But much of the Commentary should still apply, and if you have both versions side by side, it shouldn't be hard to figure out what's still relevant.
This is off the top of my head: In order to understand the methods employed in The Definition of Standard ML, you should some basic understanding of:

* [set theory](http://en.wikipedia.org/wiki/Set_theory)
* [functions](http://en.wikipedia.org/wiki/Function_%28mathematics%29)
* [first-order logic](http://en.wikipedia.org/wiki/First-order_logic)
* [type theory](http://en.wikipedia.org/wiki/Type_theory)

Additionally, you should be able to read and understand [inference rules](http://en.wikipedia.org/wiki/Inference_rules) of which the book makes extensive use.