Continuum and Fluid Mechanics each have a long history. Indeed we take some past achievements nearly for granted whenever we fly in an airplane or turn on the television to check the weather report. The wide availability of computers for research purposes makes the present a new golden age for the study of both fluid and continuum mechanics.
It is perhaps easier to define fluid mechanics than continuum mechanics. After all we are surrounded, indeed bathed in, fluids for the entirety of our lives. The actual mathematical description of fluid flow can be vastly different depending on the scales of interest. Thus, while the aerodynamics of a bumble bee's flight and the evolution of a hurricane are technically governed by the same set of equations, the simplifications made to reflect the dominant physics of each situation are wildly different.
As broad as fluid mechanics is, continuum mechanics can be considered to be even broader. This is because it is concerned with the general theory of equations that govern fluids, solids and all the exotic materials in between, from a general, and often abstract, point of view. Since much of the materials that surround us and make much of modern life possible (plastics being the most obvious example) are neither fluid nor solid, but something in between, there is also an intensely practical side to continuum mechanics. Indeed, the study of materials ranges across many disciplines in both the pure and applied sciences. One of the things we hope to convey throughout these web materials is the particular nature of studying materials within an applied mathematics setting.