Ruler And Compass 

1. Given two points, draw the straight line passing through both of them.
2. Given two (nonparallel) straight lines, find the point where they intersect.
3. Given two points, draw the circle with one as centre and passing through the other.
4. Given two circles, or a circle and a straight line, find the point or points (if any) where they intersect.
Some problems can be solved using only these operations and some can't. For instance, you can do these:
a1. Given a triangle, find a square of equal area.
b1. Construct a regular polygon with 102 sides.
but you can't do these:
a2. Given a circle, find a square of equal area.
b2. Construct a regular polygon with 100 sides.
How to distinguish the possible problems from the impossible? That's a task for the (at first glance quite unrelated) field of Galois theory...