This book presents a 100% novel approach to phraseology: A language-universal deductive calculus of all theoretically possible phraseological expressions (= phrasemes) is proposed, implemented in 51 rigorously defined notions. Nine major classes of phrasemes are established and illustrated: lexemic idioms (shoot the breeze), lexemic collocations (pay a visit; helicopter parents), lexemic nominemes (the Northern Palmyra) and lexemic clichés (What’s your name?; to put it differently); morphemic idioms (forget), morphemic collocations (Londoner ~ Muscovite), morphemic nominemes (Greenland) and morphemic clichés (antidepressant); and syntactic idioms (Her be late?!?). An additional class of pragmatically constrained lexemic expressions is described: pragmatemes (No parking; At attention!; Roger.). Each phraseme class is supplied with precise methodology for a lexicographic description; a number of lexical entries for representatives of all classes are given. The language data come from English and Russian. General Phraseology: Theory and Practice is meant as a contribution towards the elaboration of a unified notional system for linguistics.