We are going to study chaos in dynamical systems, which has a very broad range of applications! 50 years ago almost nobody thought that such phenomenon as chaos required any serious consideration and investigation, this is just randomness, right? In the last two decades this conception drastically changed. Chaotic dynamics is present not only in our everyday life but  in ALL areas of science and in fact can be and needs to be thouroughly analysed and systematised. There are different types of chaos and now we know how to distinguish between them! Also a lot of  computer programs and software are available which make a proper analysis of  chaotic dynamics possible.