Alkali
The word "alkali" is derived from Arabic "al qalīy" (or "alkali"), meaning "the calcined ashes" (see calcination), referring to the original source of alkaline substances. A water-extract of burned plant ashes, called potash and composed mostly of potassium carbonate, was mildly basic. After heating this substance with calcium hydroxide ("slaked lime"), a far more strongly basic substance known as "caustic potash" (potassium hydroxide) was produced. Caustic potash was traditionally used in conjunction with animal fats to produce soft soaps, one of the caustic processes that rendered soaps from fats in the process of saponification, one known since antiquity. Plant potash lent the name to the element potassium, which was first derived from caustic potash, and also gave potassium its chemical symbol K (from the German name Kalium), which ultimately derived from alkali.
Alkyl
In organic chemistry, an alkyl substituent is an alkane missing one hydrogen.
The term alkyl is intentionally unspecific to include many possible substitutions. 
An acyclic alkyl has the general formula CH. A cycloalkyl is derived from a cycloalkane by removal of a hydrogen atom from a ring and has the general formula CH.
Typically an alkyl is a part of a larger molecule. In structural formula, the symbol R is used to designate a generic (unspecified) alkyl group. The smallest alkyl group is methyl, with the formula CH−. Although the name 'alkyl' is strictly given to straight chain alkyls only. For branched chain alkyls, terms like "iso", "neo" are often used along with the word "alkyl".
The word root "alkyl" is encountered in several contexts. Alkylation is an important operation in refineries, for example in the production of high-octane gasoline. Alkylating antineoplastic agents refer to a class of compounds that are used to treat cancer. In such case, the term alkyl is used loosely. For example, nitrogen mustards are well-known alkylating agents, but they are more complex than a mere hydrocarbon. In chemistry, alkyl refers to a group, a substituent, that is attached to other molecular fragments. For example, alkyl lithium reagents have the empirical formula Li(alkyl), where alkyl = methyl, ethyl, etc. A "dialkyl" ether is an ether with two alkyl groups, e.g., diethyl ether (O(CH)). Alkyl also refers to an active ingredient in green algae preventatives used in swimming pools.