German physicist Georg Ohm :Ohm's law

treatise published in 1827.
described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire.

In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ is a material dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff

Microscopic origins of Ohm's law

The dependence of the current density on the applied electric field is essentially quantum mechanical in nature; 

Classical and quantum mechanical views of conductivity have both described the movements of electrons in a metallic solid. The free electron gas that is present in metallic solids is the reason for an important property of all metals: conductivity.

Solid states

Solids can be split into two groups: amorphous and crystalline 

Amorphous solid structures occur when a liquid is cooled too rapidly for the crystalline structure to form. Glass is a typical amorphous solid.
however, ample time is allowed during the cooling of a liquid, then a crystalline structure will form.
crystalline structures, several different types of bonding are possible. These include ionic bonding, covalent bonding, and metallic bonding.
structure of a specific crystal is dependent on the bonding type, along with the sizes of the atoms involved.

Paul Drude