Roger Penrose's groundbreaking and bestselling "The Road to Reality" provided a comprehensive yet readable guide to our present understanding of the laws that are currently believed to govern our universe. In "Cycles of Time", he moves far beyond this to develop a completely new perspective on cosmology, providing a quite unexpected answer to the often-asked question, 'what came before the Big Bang'? The two key ideas underlying this novel proposal are a penetrating analysis the Second Law of thermodynamics - according to which the 'randomness' of our world is continually increasing - and a thorough examination of the light-cone geometry of space-time. Penrose is able to combine these two central themes to show how the expected ultimate fate of our accelerating, expanding universe can actually be reinterpreted as the 'Big Bang' of a new one. On the way, many other basic ingredients are presented, and their roles discussed in detail, though without any complex mathematical formulae (these all being banished to the appendices). Various standard and non-standard cosmological models are presented, as is the fundamental and ubiquitous role of the cosmic microwave background. Also crucial to the discussion are the huge black holes lying in galactic centres, and their eventual disappearance via the mysterious process of Hawking evaporation.