Friction force between sliding surfaces arises due to varied and complex mechanisms and can be responsible for undesirable dynamic characteristics in many mechanical systems. Controversies over the theory of friction have been reported in the literature. Friction laws are phenomenological in charcacter since they are based on observable and measurable quantities. The mechanics of contact and friction in metal-metal and elastomer-metal contact surfaces are reviewed. Unfortunately, there is no satisfactory method capable of determining or measuring the area of contact between sliding bodies. Both dry friction and lubricated friction are considered. The modeling of the friction force in mechanical systems depends on several factors. These include the material properties and geometry of the sliding surfaces, surface roughness, surface chemistry, sliding speed, temperature, and normal load. Other factors include the effect of normal and tangential vibrations on the static friction. Here the static friction is considered as a special case of kinetic friction. This background is essential for dynamicists studying friction-induced vibration, chatter, squeal and chaos topics which will be presented in the second part.