It is a worldwide tradition to teach Solid Mechanics by referring to continuous bodies. Accordingly, ordinary and/or partial differential equations, as well as vectors and tensors, are introduced. The result is that the learners are often overwhelmed by the technicality of Mathematical Analysis, which can obscure the logical process on which Solid Mechanics is founded. This book introduces a highly innovative teaching method, consisting of analyzing the mechanics of rigid-body systems equipped with elastic (or elasto-plastic) lumped devices. Since these systems are finite-dimensional, Algebra is the only mathematical tool required. The main advantage of this new approach is that, due to the significant simplifications in calculus, the learners can focus their attention on the (complex) architecture of Solid Mechanics. Consequently, they will attend more advanced courses on continua having already assimilated the key goals, principles, and physical understanding. Several topics are addressed: kinematics and statics of rigid-body systems, elastic problems, nonlinear constitutive behavior (plastic collapse), dynamics, stability and bifurcation, as well as geometrically nonlinear phenomena. Direct formulations are presented based on congruence, equilibrium, and constitutive laws. Moreover, variational principles such as Virtual Work and Energy Principles are applied. Both the displacement method and the force method are equally discussed. Many examples and exercises are provided.