An alphabet is a way of writing in which letters, or groups of letters, represent phonemes (units of language perceived as distinct sounds in speech, such as /b/ in bat). Most modern languages use alphabets, but not all: Chinese varieties are famous for their characters, and Japanese uses a mixture of mostly Chinese-derived characters (kanji), two mora-based systems similar to syllabaries (katakana and hiragana), and a smattering of the Roman alphabet, roomaji, often seen on signage and for company names. The Korean alphabet, unlike most other alphabets, groups letters by syllables within words, which look rather like drastically simplified kanji.
The alphabet was originally developed by Semites in ancient Egypt, adapting simplified hieroglyphics to represent the consonant sounds of the Semitic languages. The Phoenician alphabet, one variant of the ancient Semitic alphabets, was adopted with significant modifications by the Greeks for their language. The major innovation of the Greeks was the use of letters to represent vowel sounds, a change which was much more useful in the Greek language than in the Semitic languages. (In Semitic languages, words which differ only by the sound of one or two vowels are usually closely related, and the correct meaning is easier to determine by context; Greek along with other Indo-European languages has many words which completely change meaning with the change of a single vowel.)
The word alphabet derives directly from the Greek name of the first two letters, alpha and beta.
A form of the Greek alphabet was adopted by the Etruscans, from whom it was adopted, with further changes, by the Romans. The Roman alphabet underwent additional changes to reach the form which is familiar today. Greek Christian missionaries developed the Cyrillic alphabet, derived from the Greek alphabet, for translating the Bible and other religious texts into Slavic languages; the Cyrillic alphabet has evolved since then, with some variations across the languages which use it.
The Phoenician alphabet inspired other alphabets in the Middle East, leading to the Hebrew and Arabic alphabets, and to other alphabets which have fallen out of use. During the early expansion of Islam, many languages unrelated to Arabic ended up being written in Arabic script, often with minor variations or additional letters to adapt the alphabet to the new languages. The Aramaic alphabet, also derived from Phoenician, evolved as it was adopted by different languages until it developed into the Brahmanic script, the basis for most of the alphabets of the Indian subcontinent. Brahmanic scripts inspired the writing systems of the Mongols, which inspired, but did not evolve directly into, the Korean alphabet.
European colonization led to the adoption of the Roman alphabet for many languages completely unrelated to the languages of the colonizers; the alphabet was often adapted by adding diacritical marks and occasionally additional letters. The Cherokee alphabet was developed by Sequoyah inspired by the Roman alphabet used by the English-speaking whites settling in Cherokee lands.
The International Phonetic Alphabet was developed by linguists to represent all sounds in all languages, and has a very large number of symbols to express all the variations of different sounds found in different languages, many of which are not found in other alphabets.