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The presented manual offers a structured exploration of vector algebra and force systems in the context of rigid body mechanics. It covers fundamental topics such as the subject and models of mechanics, vector and matrix methods for calculating force moments, and conditions for the equilibrium of rigid bodies. Special attention is devoted to Equivalent transformations of forces, theorems essential for static analysis (such as Varignon’s and Poinsot’s), and practical problem-solving using both analytical and computational techniques. The manual includes sections on the limits of equilibrium under friction forces, discusses different forms of friction, and provides interactive exercises for mastering statically determinate systems. This comprehensive resource is intended for students and professionals seeking to deepen their understanding of static equilibrium, force transformation, and mechanical modeling.