Da Vinci
Leonardo Da Vinci (1452-1519) stated the two basic laws of friction 200 years before Newton even defined what force is.  Da Vinci simply stated that: 1) if the load of an object is doubled, its friction with also be doubled; and 2) the areas in contact have no effect on friction.  These were two profound statements.  The first is stating that friction is proportional to the normal force, and the second is stating that friction is independent of cross-sectional area.  Note that the second statement is counterintuitive; most of us would assume that friction does depend upon the cross-sectional area.
He also made the observation that different materials move with different ease.  He surmised that this was a result of the smoothness of the material in question; thus, smoother materials will have smaller frictions.  Da Vinci also made some quantitative statements about friction.  He stated that, "every frictional body has a resistance of friction equal to one quarter of its weight."  In contemporary terms, the coefficient of friction is 0.25.  By today's standards we would say that wasn't even close, but for dirty materials that value is fairly accurate.  Leonardo Da Vinci did not publish his theories, so he never got credit for his ideas.  The only evidence of their existence is in his vast collection of journals.  These journals contain a lot more than just writings about friction.  In addition to his famous artwork, their are drawings of submarines, helicopters, and airplanes over 300 years before their inventions.  To learn more about the many other sides of Da Vinci check out these links.
American Museum of Natural History
Exploring Leonardo
Scientist, Inventor, Artist
Why is the Mona Lisa Smiling?.
Amontons
Guillaume Amontons (1663-1705) was an architect by training, but in those days this by no means meant that he was limited to that one field.  He designed one of the first steam engines, and he was the first to state that a certain increase of air's temperature produces a proportional increase in the air's pressure.  This led to him constructing the first gas thermometer.  Because he contracted a disease which left him deaf, Amontons developed a new system of communication.  He later used this new form of communication to invent the first form of the telegraph, called the optical telegraph.  He is important in the field of tribology because he rediscovered the two basic laws of friction that had been discovered by Leonardo Da Vinci, and he also came up with an original set of theories.  He believed that friction was predominately a result of the work done to lift one surface over the roughness of the other, or from the deforming or the wearing of the other surface.  For several centuries after Amontons' work, scientists believed that friction was due to the roughnesses on the surfaces.
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The Empirical Gas Laws and the Thermometer
Measuring Friction on an Atomic Level (disproving Amontons' Law)
The optical telegraph

Desagulier
John Theophilus Desagulier (1683-1744) had a significant impact on the study of friction.  He considered the argument of Amontons about surface roughness and made the remark that "as surfaces are made smoother they ought to slide more easily, yet it is found by experience that the flat surfaces of metals or other bodies may be so far polished as to increase friction."  He attributes this to the adhesion between the two surfaces.  He conducted experiments with lead balls that illustrated this idea.  After cutting the two balls in order to expose fresh, clean surfaces on each, Desagulier pushed the two surfaces together.  It then took 16 pounds of force to separate the lead balls.  He believed in this idea, but he was unable to explain the laws of friction relating to adhesion because he could figure out how to justify the already proven statement that friction is independent of cross-sectional area when adhesion most definitely is.

Fig. 2:  A drawing similar to this was in Desagulier's paper demonstrating how lead balls adhere to each other.
Desagulier was another person who did much more than contribute to the study of friction.  He also made significant strides in the design of the young steam engine.  After several fatal accidents involving exploding boilers, he invented the safety valve so that the pressure would not get too high.  He also designed his own engine which was very successful for the time period at raising water from a well.  This is one of his sketches of this steam pump.
Desagulier's steam pump.  Picture obtained from the following site.
To learn more about the steam engine and his contributions to it, check out The Growth of the Steam Engine.

Coulomb
Charles August Coulomb (1736-1806) also considered the idea of adhesion, but he dismissed the idea because for it to be true friction would have to be proportional to cross-sectional area.  He attributed friction to the work done to dragging one surface up the roughnesses of the other surface.  The following figures will help you to visualize his ideas.

Using the two principles shown above, Coulomb designed the first tribometer.  The tribometer is a device which measures the coefficient of friction of a certain material.  A high-tech version of Coulomb's tribometer is still used today for research on material wear and lubrication.    Coulomb worked on friction, but he is best known to physicists for his work on electricity and magnetism. He established experimentally the inverse square law for the force between two charges, which became the basis of Poisson's mathematical theory of magnetism. Coulomb also wrote on structural analysis: the fracture of beams, the fracture of columns, the thrust of arches. He also has a paper on the way sap circulates inside a tree.  He is also known to geotechnical engineers as the grandfather of soil mechanics.  If you are interested in finding out more about Coulomb, these are some great pages to get you started.
The Grandfather of soil mechanics
Coulomb's Law
Coulomb Force