“I have traversed this bottomless night, which extinguished all light and joy of my life. I entreat you, leave the science of parallel alone”, wrote a Hungarian mathematician Farkas Bolyai to his son János, horrified at the thought that his son is attracted by the problem of parallels. János was not deterred, however, and discovered, simultaneously with Lobachevski, a consistent geometry in which the Euclidean parallel postulate does not hold. We will zoom through the path of mathematical thought that took over 2000 years, noticing which results from a high school geometry text-book do not rely on the parallel postulate, and which are altered completely in hyperbolic geometry.