What is molarity, molality and normality?

, , and normality are all units of concentration.
Molarity(M) is the number of moles of dissolved in one liter of a solution and the unit for molarity is moles/L.
M = ##”moles of solute”/”liters of solution”## (Note: If you are given volume in mL or some other volume unit, you need to convert it to liters.)
Lets say you dissolve 1.00mol of a solute into 0.500L of solution. The molarity(M) would be 1.00mol/0.500L = 2.00mol/L = 2.00M
Molality( m ) is the number of moles per kilogram of . It is determined by dividing the number of moles (n) of the solute by the mass of the solvent in kg.
m = ##”moles of solute”/”mass of solvent in kg”##
Lets say you dissolve 0.75mol of a solute into 2.50L of water. Since the of water is 1.00g/mL and one liter of water is 1000mL, the mass of a liter of water is 1.00kg. So 2.50L of water has a mass of 2.50kg.
The molality, m , of this solution would by 0.75mol/2.50kg = 0.3mol/kg = 0.3 m .
Normality
Please refer to the following Wikipedia article, http://en.wikipedia.org/w/index.php?title=Equivalent_concentration&redirect=no. It gives a definition of normality and examples. It appears that normality is falling out of favor and its use is discouraged by the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST).