In each and every tutorial (which I call "lessons") I will try to make things as objective, clear and simple as possible for anyone to understand.
However do not fall under the illusion that you will understand it all overnight, as learning how to code is a gradual and phased process which may require lots of dedication at first. So don't get demotivated if you can't understand something at first, just keep trying until you do, none of the today's developers has born knowing how to make code either.

Many of these tutorials will have diagrams, images and material to test with, so you can understand the whole thing better, since theory alone is obviously worthless.
Any doubts or further tutorial requests can be put here or in the respective tutorial topics. I hope they prove to be helpful by someone.
Also, it helps a lot to start checking the actual UnrealScript source code of the engine, therefore I uploaded an organized version:
UT UnrealScript Source: http://uncodex-ut.host56.com
And for some of your doubts and better understanding of the language and the engine, you can also take a look at:
Unreal Wiki: http://wiki.beyondunreal.com/
Just be careful to double check if the information you're seeing is related to Unreal Tournament 1 and not the 2004 or III versions.
Plus, do not take all the info there as gospel, since there are a few bits of inaccurate information there. If you have any doubts concerning one of the pages there, you can post here and we will clear it out for you.
0 - The science behind mods
1 - Your first mutator
2 - Your first trigger
3 - Variables, functions and objects
4 - UnrealScript: Language
5 - UnrealScript: Variables
6 - <soon>
7 - <soon>
8 - <soon>
9 - <soon>
10 - <soon>
11 - <soon>
12 - <soon>