Lime is a collective name for minerals (salts) of calcium as lime (lime paste, living lime), slaked lime (whitewash, fat lime, air lime, hydrated lime, calcium hydroxide Ca (OH)2), chalk (calcium carbonate, CaCO3), marl and gypsum (calcium sulfate, CaSO4).
Lime is derived from lime stone and shells.
In lime kilns, the calcareous mass is burned at about 900 degrees C.
Limestone (CaCO3) then decomposes into calcium oxide CaO (quicklime) and carbon dioxide (CO2).
Lime reacts violently with water (corrosive on the hand).
Embers are separated from the quicklime.
The calcium oxide is slaked of with water to form calcium hydroxide (Ca (OH)2 = slaked lime, also simply referred to as lime.

limestoneBy adding a little water lime powder is created.
By adding more water strongly alkaline lime paint (pH 12.5) arises. Because of the carbonization with CO2, the pH drops to about 8. This high pH values make​, the product is fungicidal, bactericidal and antiseptic.

Previously mortar was made by baking limestone. The Romans improved the air lime, by adding inert volcanic ash, trass and /or brick powder. Thus, they were given a hydraulic binder, an intermediate form of air-slaked lime, and in fact real cement.

There are 2 types of lime
Air- or hydrated calk (calcium carbonate) is pure is lime, calcined limestone, which (slowly) hardens to air.
Air Lime is burned out fairly pure limestone .

Hydraulic lime contains clay, it reacts and hardens in the presence of water (even on the air humidity), and is cured not soluble in water. Other hydraulic materials are cement and pozzolans (e.g. trass).

Pure hydraulic lime is made by burning limestone that naturally contains minerals and clays that convert into silicates and calcium aluminates during the burning process. After calcination and hydration of the stone a binder is created with next to a lime air curing share a water-reactive hydraulic share.
For example, lime mortar is made by adding an inert material such as tuff, trass, crushed brick or gravel to slaked lime.
Artificial hydraulic lime is made by grinding clinker limestone of filler, gypsum as binding controller, and an additive to make the mortar workably and waterproof. It looks like natural hydraulic lime.

Chalk can be seen as the solid material from lime.