Does the universe have the beginning and end How does it evolve The present cosmology has become precise science to answer much of those curious and fundamental questions. We introduce historical development leading to the “Big Bang” cosmology. The Big Bang cosmology naturally gives some puzzles as well as explanation on various phenomena in the universe. Some can be answered by the inflationary universe model. However still some fundamental questions remains: The present universe consists of mostly so-called dark energy and dark matter, not discovered yet, and cannot be explained within the Standard Model of particle physics. Moreover, the modern physics and gravity theory breaks down as we get too close to the initial moment of “Big Bang”. We finally introduce the string theory and discuss whether it can resolve these new challeges.