Cooling atomic gases to nanokelvin temperatures has revolutionized atomic physics. At such low temperatures, the weak forces between atoms in a dilute gas become dominant and lead to new forms of strongly correlated matter. Ultracold fermions develop behavior analogous to electrons in superconducting materials. A new form of high-temperature superfluidity has been discovered. Ultracold atoms in periodic potentials formed by laser beams can have properties of liquids or insulators. In the future, we plan to use ultracold gases to create designer matter, i.e. to realize new forms of matter in the laboratory which have been discussed as model systems for many-body phenomena, but have not been observed in nature.