Shaft in Transmission Energy

Ok, you did not mention any specific question, I'll try to explain some things in a simple way, then you come back woth your doubts.

What are the advantages and disadvantages between the solid and hollow shaft?

R: It's not a matter of hollow or solid, but what's the geometry of the cross sectional areal (the inertia moment related to the cross section neutral line), and what's the cross sectional area itself. A built structure stiffness and resistance depends on the material used and the geometry, the profile used and the load conditions. The chalenge is to find the lighter and stiffer (and cheaper) profile for the application you have.

classify the shafts based on its shape and the applications.
R: There are round, square, rectangle, I, C, L, tube, hexagonal, etc. There are no classifications foe geometric figures. Due to the geometry simmetry, tube and round shafts are used when you have torque transmission or combined mechanical loads. When the loads are to be applied in pre-determined directions, maybe an I profile or square tube is better. When load is purelly traction, you can use solid shafts because they're cheaper and use less space for the same amount of material. But it's too general gidelines, for more detailed information, post your problem.

is it heat treatment and surface hardening applied to shaft...how it affect the quality of shaft
R: Of course, depending on the material from what the shaft is being built. Have you heard about heat treating plastic or a carbon-fiber composite? Again, it's not "the shaft", depends on the material of what it's built, and what do you need in your application (surface hardness, core hardness, high strengh, high toughness, etc).

and what means by shaft under static and fluctuating loading?

R: It's what your question mentions. Static is when the load is static, constant, or almost. Fluctuating loading is when your load varies over the time. You can also consider impact. The speed and number of cycles a load is applied to a specimem affect its behaviour, in what we call fatigue. Can be of high cycle, low cycle, environment assisted, there are really a lot of things to make things go wrong for you. Again, post your specific doubts.

Well say bhrescobar, here is something to add ons:

Hollow shaft would be stronger for bending and torsion in term of unit weight (less weight = cheap) when compare to solid shaft. But hollow shaft are not easily available (or in other words = expensive to produce), bigger diameter of hollow shaft also mean bigger shaft component (bearing etc) ==> more expensive. Normally it is very obvious which one is better but in some case you need to do detail study in order to determine what kind of shaft to used.

Depend on the shaft usage, shaft may needs surface hardening, like it term explain, it will harden the surface, but you will sacrifice the ductility and make the shaft more expensive. Normally I won't heat treatment a shaft unless it really needs.

There is a lot of term for loading, static vs dynamic, live vs dead, constant vs fluctuating etc. Static normally means load that won't varies, as oppose to dynamic, Fluctuating is like what bhrescobar said.