An analytic language is a type of natural language which breaks up concepts into a series of root/stem words accompanied by prepositions, postpositions, particles and modifiers, using affixes very rarely, as opposed to synthetic languages which synthesize lots of various concepts into a single word, using affixes regularly. Syntactic roles are assigned to words primarily by the word order. For example, by changing the individual words in the Latin phrase "Feles piscem cepit" ("cat caught a fish") to "Felis piscis cepit" ("cat was caught by a fish"), piscis becomes the subject, while felis becomes the object. This transformation is not possible in an analytic language without using the passive voice and the word "by", or altering the word order. Typically, analytic languages have a low morpheme-per-word ratio, especially with respect to inflectional morphemes. No natural language however is purely analytic or purely synthetic.
The term analytic is commonly used in a relative rather than an absolute sense. The most prominent and widely used Indo-European analytic language is Modern English, which has lost much of the inflectional morphology that it inherited from Proto-Indo-European, Proto-Germanic and Old English over the centuries and has not gained any new inflectional morphemes in the meantime, which makes it more analytic than most other Indo-European languages.
For example, Proto-Indo-European had much more complex grammatical conjugation, grammatical genders, dual number and inflections for eight or nine cases in its nouns, pronouns, adjectives, numerals, participles, postpositions and determiners, Standard English has lost nearly all of them (except for three modified cases for pronouns) along with genders and dual number and simplified its conjugation.
Latin, Spanish, German, Greek, Russian and majority of the Slavic languages, characterized by free word order, are synthetic languages. Nouns in Russian inflect for at least six cases, most of which descended from Proto-Indo-European cases, whose functions English translates by instead using other strategies like prepositions, verbal voice, word order, and possessive 's.
Modern Hebrew is much more analytic than Classical Hebrew with both nouns and verbs.
A related concept is that of isolating languages, which are those with a low morpheme-per-word ratio (taking into account derivational morphemes as well). Purely isolating languages are by definition analytic and lack inflectional morphemes. However, the reverse is not necessarily true, and a language can have derivational morphemes but lack inflectional morphemes. For example, Mandarin Chinese has many compound words, which gives it a moderately high ratio of morphemes per word, but since it has almost no inflectional affixes at all to convey grammatical relationships, it is a very analytic language.
English is not totally analytic in its nouns since it uses inflections for number (e.g., "one day, three days; one boy, four boys") and possession ("The boy's ball" vs. "The boy has a ball"). Mandarin Chinese, by contrast, has no inflections on its nouns: compare 一天 yī tiān 'one day', 三天 sān tiān 'three days' (literally 'three day'); 一個男孩 yī ge nánhái 'one boy' (lit. 'one [entity of] male child'), 四個男孩 sì ge nánhái 'four boys' (lit. 'four [entity of] male child'). Instead, English is considered to be weakly inflected and comparatively more analytic than most other Indo-European languages.
Persian could be considered an analytic language. Generally, there are no inflections as we know it. There is a system of prefixes and suffixes that connect the words to express possession or attribute a quality. They could be integrated in the word in writing while they keep their function. For example, the suffix ها hâ makes the words plural like English s: دختر ها آمدند dokhtar hâ âmadand 'The girls came'. Persian has no agreement of a noun's or adjective's number or gender in many other languages because it is inherently a genderless language. Practically, there are no inflections for numbers keeping the above example; یک روز yek rooz 'one day', سه روز se rooz 'three days' (literally 'three day'), یک پسر yek pesar 'one boy' (lit. 'One boy'), چهار پسر čahâr pesar 'four boys' (lit. 'Four boy'). Similarly, there are no inflections for possession as well. A short '-e' sound (a diacritical mark) ـِ -e is added after a word starting with a consonants letter to show that it is possessed by (or belongs to) the next word so 'The boy's ball' would be توپِ پسر toop -e pesar. However, the diacritical mark 'ـِ' is put under the last letter of the first word for beginners and in written literature and everyday publications. It is otherwise usually omitted but pronounced in reading. For words ending with long vowels, the letter ی is added with a short '-e' sound written as یِ as a suffix. Thus, 'The boy's foot' would be پا یِ پسر pa -ye pesar. However, in literature and daily writing, the letter is omitted although it is pronounced in reading. The same system is used to connect adjectives and nouns to words.