A major objective of this monograph is to present an agent-based simulation of artificial populations. The focus is on possible unexpected or catastrophic events that may spontaneously appear in simulations. A short recall of the tenets of the theory of catastrophes is given. Several examples of artificial society simulations are provided as the main topic of the book. With agent-based modeling, possible catastrophes and unexpected events in artificial populations are simulated. The book presents a new modeling and simulation tool, applied to social system simulation. The models are coded in the object- and agent-oriented language Bluesss (Blues Simulation System), related to the C++ language. The program code consists of a series of generic declarations of processes. Each of them includes a number of events that are coded in C++. At the runtime, a population of objects is generated. All the objects (agents) start to execute their own events, and interact with one another. During the simulations it is possible to observe the macro-behavior of the population, where some unexpected or "catastrophic" events occur. The examples include a stock market crash, catastrophes in extended prey-predator systems, growing organisms and cancer, epidemics, social inequality and economic decay, mass-service systems, and more. Remarks on possible simultaneous events are also included.