Designing an adaptive optics (AO) system for extremely large telescopes (ELT's) will present new optical engineering challenges. Several of these challenges are addressed in this work, including first-order design of multi-conjugate adaptive optics (MCAO) systems, pyramid wavefront sensors (PWFS's), and laser guide star (LGS) spot elongation. MCAO systems need to be designed in consideration of various constraints, including deformable mirror size and correction height. The y,{bar y} method of first-order optical design is a graphical technique that uses a plot with marginal and chief ray heights as coordinates; the optical system is represented as a segmented line. This method is shown to be a powerful tool in designing MCAO systems. From these analyses, important conclusions about configurations are derived. PWFS's, which offer an alternative to Shack-Hartmann (SH) wavefront sensors (WFS's), are envisioned as the workhorse of layer-oriented adaptive optics. Current approaches use a 4-faceted glass pyramid to create a WFS analogous to a quad-cell SH WFS. PWFS's and SH WFS's are compared and some newly-considered similarities and PWFS advantages are presented. Techniques to extend PWFS's are offered: First, PWFS's can be extended to more pixels in the image by tiling pyramids contiguously. Second, pyramids, which are difficult to manufacture, can …