The thesis describes Fibonacci numbers, golden ratio, their properties and how they can be used in computer sciences. Fibonacci numbers are closely related to the golden number as the ratios of two consecutive Fibonacci numbers approach the golden number. We can calculate Fibonacci numbers by recursion, Fibonacci Q-matrix or with an explicit formula called Binet's formula. This formula is not the best approach, because we get large numerical errors for larger numbers. There are many interesting relations between Fibonacci numbers and prime numbers. One of them is that all Fibonacci numbers, except four special cases have a prime divisor that does not divide any previous Fibonacci number, this property is explained in detail in this thesis. The question whether there are infinitely many Fibonacci primes is currently an unsolved problem in mathematics. Another special property of Fibonacci numbers, explained in Zeckendorf's theorem, is the fact that every positive integer can be written uniquely as a sum of Fibonacci numbers. This theorem induces a binary code known as Fibonacci code.
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