Analytic - little inflection, rely on word order or auxiliary words to convey meaning.
E.g. English (mostly), Mandarin.
Synthetic - not analytic.
Agglutinative language - type of synthetic; words are formed by stacking morpemes without changing their spelling or meaning. E.g Turkish, Uzbek, Korean.
Fusional language - type of syntheric; single morpheme can denote multiple grammatical or semantic features. E.g. Russian, Spanish.
Inflection - word formation, words are modified by gender, number, tense, mood, etc.