Slitherlinks are one of 20+ puzzle types invented by or first published by the Japanese puzzle firm Nikoli.
The rules are simple: draw one line through the grid, in such a way that
a) it forms one closed loop, and
b) in each cell the number of borders matches the number in the cell, and
c) the loop may not touch itself, not even its corners.
So try your hand at a small puzzle:
The last one is a screenshot from the Loopy program, which you can freely download from Simon Tatham sportabel puzzle collection.