As we enter an exciting new era in industrial design, simulation, and manufacturing, a clear understanding of mechanics of solids is needed now more than ever. This primer is a condensed synopsis of basic undergraduate mechanics and is designed to supplement classical textbooks in this area. The focus is on the essentials of mechanics, specifically: • The concept of stress. • Stress-strain relationships. • Failure theory. • Axial loading of a rod. • Transverse (bending) loading of a beam. • Industrial application: modeling of 3D printing. • Transverse shear stresses. • Torsional loading of a rod. • Pressure vessels. • Buckling of columns. • The basics of finite element methods. • A unifying concept: continuum mechanics.