Statics of constrained systems of rigid bodies is studied. First, sets of forces (lumped or distributed) applied to a free rigid body, frozen in a fixed reference configuration, are considered. The notion of moment of a force (or torque) with respect to a point is introduced. Based on the Cardinal Equation of Statics, it is recognized that systems of forces having the same resultant vector and resultant moment are equivalent. Elementary equivalence operations are illustrated, leading to define generalized force components, six in-space and three in-plane for each body constituting the system. Next, reactive forces are defined by invoking the Postulate of Perfect Constraints, which subordinates the mechanical performance of a constraint (i.e., the kind of reaction provided) to its kinematic performance (i.e., the displacements prevented). Planar and spatial constraints are illustrated. Third, the Static Problem is formulated, consisting of evaluating the reactive forces equilibrated with the active forces, supposed known. According to the Rouché-Capelli Theorem, systems are classified as: statically determined, under-determined, over-determined and degenerate, for each of which the solutions to the static problem (if any, and possibly not unique) are found. Static and kinematic classifications are then compared, so far based on examples, and important symmetry properties are discovered. As particular reactive forces, the internal solicitations are defined, a concept useful for rigid beam analysis. Strategic methods of solution of the static problem, oriented to a manual approach, are discussed.