The task of any physical theory is to develop the means to predict the results of the measurements of a physical quantity sometime in the future based upon the information about the current state of the system under study and knowledge about interaction of this system with its environment. The term “state” has many different uses in physics—it is used to describe different states of matter (solids, liquids, etc.)—in thermodynamics we derive various equations of state, relations between various thermodynamic parameters. We can also talk about a particular state of a system, meaning specific values of a set of quantities important for a problem at hand. In this book I will consider, for the most part, systems consisting of a small number of particles, placed in a variety of different environments. The states, which I will be dealing with here, are “mechanical states,” but the precise meaning of this term depends upon the choice of a conceptual framework, classical or quantum, with which the problem is approached.