The chapter presents preliminary results of a quantitative analysis of two patterns of complexity growth in the Big History—decelerating universal (cosmic) evolutionary development evidenced in the Universe for a few billions of years after the Big Bang (around 13.8 billion BP) and accelerating global (biosocial) evolutionary development observed for about 4 billion years on the planet Earth since the emergence of life on it and until the early 1970s. It is shown that the first pattern can be described with an astonishing accuracy (R2 = 0.999996) by the following equation: y = C1/(t − t1*), where y is the rate of the universal complexity growth (measured as a number of phase transitions [accompanied by the growth of complexity] per a unit of time), C1 is a constant, and t − t1* is the time since the Big Bang Singularity (t1* ~ 13.8 billion years BP). In the meantime, it was earlier shown that the second pattern could be described with an almost as high accuracy (R2 = 0.9989–0.9991) by the following equation: y = C2/(t2* − t), where y is the rate of accelerating global (biosocial) evolutionary development, C2 is another constant, and t2* − t is the time till the twenty-first-century Singularity (t2*, estimated to be around 2027, or 2029 CE). Thus, the post-Big-Bang hyperbolic decrease of universal complexity growth rate and the hyperbolic increase of the growth rate of global complexity in the last 4 billion years proceeded following the same law. We are dealing here with a perfect symmetry: (1) the rate of the universal (cosmic) complexity growth decreases when we move from the Big Bang Singularity, whereas the rate of the global complexity growth increases when we approach the twenty-first-century Singularity; (2) more specifically, as the time since the Big Bang Singularity increases n times, the universal (cosmic) complexity growth rate decreases the same n times, whereas when the time till the twenty-first-century Singularity decreased n times, the global complexity growth rate increased the same n times. A somehow more complex symmetry is observed as regards the interaction between energy dynamics and complexity growth within both processes. This suggests the identification of the following eons of the Big History: (1) eon of the hyperbolic deceleration of the universal complexity growth (from the Big Bang Singularity till 4 billion YBP); (2) eon of the hyperbolic acceleration of the global complexity growth (from 4 billion YBP till the early 1970s); (3) eon of the hyperbolic (?) deceleration of the global complexity growth (from the early 1970s till ?). Finally, Korotayev goes on to propose a full Big History periodization on the basis of the complexity growth patterns and phases. Within the proposed periodization, the whole course of the Big History is subdivided into three eons identified on the basis of the complexity growth pattern that is characteristic for the respective eon; each eon is subdivided into eras identified on the basis of the complexity growth driver that was typical for the respective era; and, finally, each era is subdivided into epochs identified on the basis of the highest level of complexity achieved within the respective epoch (thus, the borders between epochs correspond to complexity jumps such as the Big Bang nucleosynthesis, recombination, emergence of the first stars, “Neoproterozoic Revolution”, Cambrian explosion, Upper Paleolithic Revolution, transition from foraging to food production, Axial Age and so on).