Kief is many trichomes that have fallen from the bud. Hash is the trichomes compressed.
Hashish (from Arabic: حشيش ḥashīsh, lit. "grass"; also hash or many slang terms) is a preparation of cannabis composed of the compressed trichomes collected from the cannabis plant. It contains the same active ingredients as cannabis (but in higher concentrations than other parts of the plant), produces the same type of psychoactive effects and is mostly illegal in the same extent; see the main article Cannabis (drug).
Hashish is often a solid or paste-like substance, of varying hardness and pliability, and will soften under heat. Its colour can vary from green, black, reddish brown, or most commonly light to dark brown. It is consumed in much the same way as cannabis buds, often being smoked in joints mixed with tobacco or cannabis buds, or in smoking pipes, or vapourized. It can also be eaten or used as an ingredient (baked into cookies or cakes, or added to stews and chocolate).