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Lubrication and binding: the mucus in saliva is extremely effective in binding masticated food into a slippery bolus that (usually) slides easily through the esophagus without inflicting damage to the mucosa. Saliva also coats the oral cavity and esophagus, and food basically never directly touches the epithelial cells of those tissues.
Solubilises dry food: in order to be tasted, the molecules in food must be solubilised.
Oral hygiene: The oral cavity is almost constantly flushed with saliva, which floats away food debris and keeps the mouth relatively clean. Flow of saliva diminishes considerably during sleep, allow populations of bacteria to build up in the mouth -- the result is dragon breath in the morning. Saliva also contains lysozyme, an enzyme that lyses many bacteria and prevents overgrowth of oral microbial populations.
Initiates starch digestion: in most species, the serous acinar cells secrete an alpha-amylase which can begin to digest dietary starch into maltose. Amylase does not occur in the saliva of carnivores or cattle.
Provides alkaline buffering and fluid: this is of great importance in ruminants, which have non-secretory forestomachs.
Evaporative cooling: clearly of importance in dogs, which have very poorly developed sweat glands - look at a dog panting after a long run and this function will be clear.