This compendium provides a broad introduction of original immersed boundary methods and current extension in computational mechanics communities. It highlights a comprehensive review of immersed methods in the context of computational fluid and solid mechanics.Most importantly, the appendix includes a complete two-dimensional working Fortran 90 immersed continua code with implicit matrix-free Newton Krylov iteration for compressible fluid and solid systems.This invaluable title will provide useful reference materials and an interesting read for academics, researchers, professionals and students.