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.