From the beginning of human history, the appearance of mathematics and the connection of numbers with the creation of everything that surrounds a human being has been noticed. The close connection between mathematics and nature has always existed even before humans began to explore it. The development of mankind has greatly influenced the very development of mathematics as a science. Number systems and numbering come in later history with the need for more complex mathematical communication. With the appearance of number systems comes the need for clearer writing and understanding of said systems. Fibonacci numbers and its system are one of those systems described in this paper. The derived formulas are formed from the properties of Fibonacci numbers and serve to facilitate computations within the system itself. The aim of this paper is primarily to get acquainted with Fibonacci numbers and series, as well as to describe interesting phenomena of these numbers in nature and history.