If friction is independent of surface area, then why do they mention in books that a circular wheel has lest less friction than a cube... and that is the reason why primitive people started using logs for transport.?

In this scenario you have to look at the shape of a wheel and cube. Try imagining cars with cubes for wheels. Not only do you have to overcome static friction, you must overcome the torque required to turn the wheels over for the first time. In this case it is about the shape.

When moving, a cube slides on one of its faces; while a log or a wheel roll, not slide. These are two different kinds of motion. Friction plays important role in both kinds of motion, though. However, in the case of the cube the friction is against you, while the same force of friction is the reason why the wheel rolls instead of sliding.