This puzzle is quite fun. Unlike those many puzzles provided in magazines and paperbacks which are solved by placing only characters or numbers, it presents you a new feeling to solve puzzles --- simply drawing lines to eventually make a big loop and the process shows you a sort of planar spacial expansion.
Its rule is very simple, but it does't mean it's easy. This makes Slither Link very good puzzle.
Before you get used to this puzzle, you might feel like you don't have a clue. But if you keep on solving many of them, you will find rules for certain situations and it will be a piece of cake to solve. Those rules are called theorem, but to avoid difficult expressions we'd like to use a term "rule" to explain why there are regular way to draw lines at certain patterns.
Actually I'm not that good at this puzzle, but I can solve most of them smoothly. My wife solves them much faster than I. When I buy a book of Slither Link questions and leave it at home, she solves last half of 100 questions in a few days. She says the first half is too easy to solve.
I had to ask her how to solve them quickly. But most of the time her explanation was "it cannot be other than this," so I'm trying to explain those know-how, my wife's rule, in details.
When you learn all of these rules, it will be much easier to solve puzzle books published by Nikoli and Gijyutsu-Hyoron Co., Ltd.. You will be much skilled and you may not want to open easy books published by Nihonbungeisha. You may want larger and more difficult questions. You don't need to worry about it. I am going to provide questions gradually for skilled users with Java. However, since Java is not suited for providing huge questions, I'm going to consider about supporting post script version which is good for printing out. Well, I'm only going to consider it and don't guarantee about postscript version...