The Fibonacci sequence is a series of numbers named after Leonardo Fibonacci. Sequence consists of numbers where each following number is the sum of the two previous numbers. Fibonacci sequence is noticeable on example of breeding rabbits. Binet formula serves us for finding nth member of the sequence. Lucas, Tribonacci, Tetranacci numbers are forms of generalization of the Fibonacci sequence. This sequence has many properties and some of them are presented in this paper. Using continued fractions it is possible to approximate irrational number alpha=(1+\sqrt(5))/(2) , which is a part of Binet formula with rational numbers. Adding up the elements in one direction, at the angle of 45 degree on Pascal's triangle we get Fibonacci numbers. The golden ratio on the example of length is defined as the ratio of parts of the length in which the entire length refers to the larger part as the larger relates to the smaller and amounts to 1,61803398874.... Golden ratio is visible in geometry on golden triangle, which is the characteristic triangle of the decagon, golden rectangle, whose sides are the lengths of the adjacent Fibonacci numbers. We also mentioned the golden angle that is 137.5 degree. Fibonacci numbers in nature can be found in flower petals, the number of spirals on pine cones, sunflowers, pineapple. A golden spiral that can be drawn in a golden rectangle is visible on the example of the nautilus, galaxies and many art paintings such Mona Lisa. We can find golden ratio on the human body. In architecture golden ratio is seen in the shape of golden rectangle on some ancient buildings, as well as modern ones.