1. Introduction to Enriched Finite Element Methods 2. Review of the Finite Element Method 3. The P-Version of the Finite Element Method 4. The Generalized Finite Element Method 5. The Discontinuity-Enriched Finite Element Method 6. Approximation Theory for PoU Methods 7. Computational Aspects of the Generalized Finite Element Method 8. Approximations for Weak Discontinuities 9. Generalized Finite Element Method Approximations for Fractures 10. Applications to Microstructural Features 11. Bridging Scales with the Generalized Finite Element Method