(From Wikipedia) "A material's property (or material property) is an intensive property of some material, i.e. a physical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another can be compared, thereby aiding in materials selection"
The number of properties is really large and all them can be measured through standardized methods, and expressed in the appropriate units.
For a first approach to materials properties we've selected the properties below:
Hardness (wikipedia link): Is the resistance of a material to indentation (penetration) or abrasion (scratching): Concrete and ceramic materials in general are very hard, some metals and alloys are also hard. Plastics and wood are soft (have low hardness). The hardest materials known to date include: Natural and synthetic diamonds, Tungsten carbide and Carbon nitride. The main applications of superhard materials include: Cutting tools, abrasives, wear-resistant coatings.
There are many techniques to measure hardness, the most direct and simple one might be the Rockwell hardness test type C, in which the hardness is the depth of the indentation made by a conical diamond penetrator subjected to a150Kp force. Every 0,002mm in depth correspond to a degree in hardness, being the maximum depth 0,2 mm (a degree of 100 in the Rockwell hardness scale). Diagram and pictures.
Toughness (wikipedia link): Is mechanical energy absorbed by a material before breaking. To be tough a material must be at the same time strong and ductile, ceramic materials are strong but break under slight deformations that's why they arent tought, on the other hand steel and titanium are tough because they are both strong and ductile. Toughness is a good property for materials subjected to impacts and strong foces that change rapidly: structures, tools and machine's moving parts.
The simplest way to measure toughness is through the Charpy test. In this test we masure the energy lost by a heavy pendulum after breaking a standadized specimen of the material under test.
Elasticity, ductility and brittleness:
Gold. The most malleable and ductile of metals.