This article deals with a brief history of Fibonacci's life and career. It includes Fibonacci's major mathematical discoveries to establish that he was undoubtedly one of the most brilliant mathematicians of the Medieval Period. Special attention is given to the Fibonacci numbers, the golden number and the Lucas numbers and their fundamental properties with enlightening examples. A large number of exciting applications of these numbers to mathematical, physical, biological and engineering sciences is included. It also contains a wide variety of material accessible to college and even high school mathematics students and teachers at all levels. Included is also mathematical information that puts the professionals and prospective mathematical scientists at the forefront of current research. (Contains 8 figures.)