Waves can be classified as either progressive or standing waves, with progressive waves transferring energy continuously in the direction of propagation without changing amplitude and standing waves forming stationary patterns. There are two main types of waves - transverse waves where the particle displacement is perpendicular to the direction of propagation, such as water ripples and electromagnetic waves, and longitudinal waves where particle displacement is parallel, including sound waves, seismic waves, and elastic waves that propagate through solids. The document discusses the different types of waves and their applications in technologies like radio, television, communications, cooking, lighting, medical imaging, and more.