This document summarizes key concepts from a lecture on mechanics and materials, including: 1. Equations relating force, deformation, and compatibility for a bar under uniaxial loading. Small angle approximations are introduced. 2. Stress is defined as force per unit area, and strain is defined as the change in length per original length. Materials have a linear elastic region defined by Young's modulus E. 3. Typical values of Young's modulus E are provided for common materials like steel, aluminum, and composites. Material selection involves optimizing stiffness k for a given application based on E and density.