In 1995, after many failures attempts and after overcoming several obstacles, it was possible cool down a gas of alkali atoms at temperature on the order of 10-7 K. For this temperature the atoms bond together to form the Bose-Einstein Condensate (BEC). The BEC is another state of matter and its properties are being studied today. The BEC was predicted by Einstein (1924) when he analyzed the work of N.S. Bose (about statistical mechanics) but it had to wait for the development and improvement of the techniques to cool and trap atoms, in 1980’s y 90’s. In this work, we’ll review those some of these techniques and other elements for BEC formation. In recognition of their work, at 2001, E. Cornell (USA), C. Weimann (USA) & W. Ketterle (Germany) were awarded with the Nobel Prize in Physics for the discovery of BEC; the fifth state of matter.