Hardness
Hardness refers to various properties of matter in the solid phase that give it high resistance to various kinds of shape change when force is applied.  Hard matter is contrasted with soft matter.
Macroscopic hardness is generally characterized by strong intermolecular bonds.  However, the behavior of solid materials under force is complex, resulting in several different scientific definitions of what might be called "hardness" in everyday usage.
In materials science, there are three principal operational definitions of hardness:
- Scratch hardness: Resistance to fracture or plastic (permanent) deformation due to friction from a sharp object
- Indentation hardness: Resistance to plastic (permanent) deformation due to impact from a sharp object
- Rebound hardness: Height of the bounce of an object dropped on the material, related to elasticity.
In physics, hardness encompasses:
- Elasticity, plasticity, viscosity, and viscoelasticity
- Strength and strain
- Brittleness/ductility and toughness

# Materials science
In materials science, hardness is the characteristic of a solid material expressing its resistance to permanent deformation. Hardness can be measured on the Mohs scale or various other scales. Some of the other scales used for indentation hardness in engineeringRockwell, Vickers, and Brinellcan be compared using practical conversion tables.

## Scratch hardness
In mineralogy, hardness commonly refers to a material's ability to penetrate softer materials. An object made of a hard material will scratch an object made of a softer material. Scratch hardness is usually measured on the Mohs scale of mineral hardness. One tool to make this measurement is the sclerometer.
Pure diamond is the hardest known natural mineral substance and will scratch any other natural material.  Diamond is therefore used to cut other diamonds; in particular, higher-grade diamonds are used to cut lower-grade diamonds.
The hardest substance known today is aggregated diamond nanorods, with a hardness 1.11 times diamond. Estimates from proposed molecular structure indicate the hardness of beta carbon nitride should also be greater than diamond (but less than  ultrahard fullerite).  This material has not yet been successfully synthesized.

## Indentation hardness
Primarily used in engineering and metallurgy, indentation hardness seeks to characterise a material's hardness; i.e. its resistance to permanent, and in particular plastic, deformation. It is usually measured by loading an indenter of specified geometry onto the material and measuring the dimensions of the resulting indentation.
There are several alternative definitions of indentation hardness, the most common of which are
- Brinell hardness test (HB);
- Janka Wood Hardness Rating;
- Knoop hardness test (HK) or microhardness test, for measurement over small areas;
- Meyer hardness test;
- Rockwell hardness test (HR), principally used in the USA;
- Shore durometer hardness, used for polymers;
- Vickers hardness test (HV), has one of the widest scales;
- Barcol hardness test, for composite materials, scale from 0 to 100.
There is, in general, no simple relationship between the results of different hardness tests. Though there are practical conversion tables for hard steels, for example, some materials show qualitatively different behaviours under the various measurement methods.
Hardness increases with decreasing particle size. This is known as the Hall-Petch effect. However, below a critical grain-size, hardness decreases with decreasing grain size. This is known as the inverse Hall-Petch effect.
For measuring hardness of nanograined materials, nanoindentation is used.
In the December 4, 2005 issue of The Jerusalem Post, Professors Eli Altus, Harold Basch and Shmaryahu Hoz, with doctoral student Lior Itzhaki reported the discovery of a polyyne that is 40 times harder than diamond. It is a "superhard" molecular rod, comprised of acetylene units.
It is important to note that hardness of a material to deformation is dependent to its microdurability or small-scale shear modulus in any direction, not to any rigidity or stiffness properties such as the bulk modulus or Young's modulus.  Scientists and journalists often confuse stiffness for hardness, and spuriously report materials that are not actually harder than diamond because the anisotropy of their solid cells compromise hardness in other dimensions, resulting in a material prone to spalling and flaking in squamose or acicular habits in that dimension. e.g., Osmium is stiffer than diamond but is as hard as quartz. In other words, a claimed hard material should have similar hardness characteristics at any location on its surface.

## Rebound hardness
Also known as dynamic hardness, rebound hardness measures the height of the "bounce" of a diamond-tipped hammer dropped from a fixed height onto a material.  The device used to take this measurement is known as a scleroscope.
One scale that measures rebound hardness is the Bennett Hardness Scale.

# Physics
In solid mechanics, solids generally have three responses to force, depending on the amount of force and the type of material:
- They exhibit elasticitythe ability to temporarily change shape, but return to the original shape when the pressure is removed.  "Hardness" in the elastic rangea small temporary change in shape for a given forceis known as stiffness in the case of a given object, or a high elastic modulus in the case of a material.
- They exhibit plasticitythe ability to permanently change shape in response to the force, but remain in one piece.  The yield strength is the point at which elastic deformation gives way to plastic deformation. Deformation in the plastic range is non-linear, and is described by the stress-strain curve.  This response produces the observed properties of scratch and indentation hardness, as described and measured in materials science. Some materials exhibit both elasticity and viscosity when undergoing plastic deformation; this is called viscoelasticity.
- They fracturesplit into two or more pieces.  The "ultimate strength" or toughness of an object is the point at which fracture occurs.
Strength is a measure of the extent of a material's elastic range, or elastic and plastic ranges together.  This is quantified as compressive strength, shear strength, tensile strength depending on the direction of the forces involved. Ultimate strength is measure of the maximum strain a material can withstand.
Brittleness, in technical usage, is the tendency of a material to fracture with very little or no detectable deformation beforehand.  Thus in technical terms, a material can be both brittle and strong.  In everyday usage "brittleness" usually refers to the tendency to fracture under a small amount of force, which exhibits both brittleness and a lack of strength (in the technical sense).  For brittle materials, yield strength and ultimate strength are the same, because they do not experience detectable plastic deformation.  The opposite of brittleness is ductility.
The toughness of a material is the maximum amount of energy it can absorb before fracturing, which is different than the amount of force that can be applied.  Toughness tends to be small for brittle materials, because it is elastic and plastic deformations that allow materials to absorb large amounts of energy.
Materials whose properties are different in different directions (because of an asymmetrical crystal structure) are referred to as anisotropic.

# Examples of hard matter
- Ceramics
- Composites
- Metals
- Semiconductors