The compression system is a major working part of any gas turbine and, aerodynamically, it is the most complex. Its successful operation in all segments of a mission is critical. In this chapter, we address the duties and lay out the fundamentals of compressor design and definitions of performance parameters. We emphasize the construction and interpretation of velocity diagrams, a vital element in any engineer’s understanding, from which a great deal can be learned about performance and trends caused by simple changes. We derive and explain the three non-dimensional stage characteristics: loading coefficient, flow coefficient and stage reaction. We then discuss preliminary compressor design addressing diffusing flow, limits on turning, deviation and the resulting blockage and mean line analysis. We give a brief history of mean line design codes and their intrinsic loss models, before tackling flow features in a blade passage and the loss elements themselves. We cite two mean line codes, CSPAN and that used in GasTurb and use them to illustrate how total pressure losses are accounted for in practice. Finally, compressor design envelopes are introduced as a means of managing multiple design limits simultaneously.