A way to form an adverb. "In xxxx-ish way", "in a way typical for xxxx" or "characterized by xxxx", when XXX is an adjective (except -ский adjectives!!!!). Cf. "По-моему", "по-твоему". "По-быстрому" - in quick manner. Cf. also the similar constiruction from nouns and -ский adjectives wothout dative: по-французски. where 'француз' - a French person. I suspect it means 'in the way French people do', and -французски is a case form (non-dative) of the short form of 'французский'. Which is a kind of possessive adjective form француз.

Thanks Ilya.

In general case, по-ххххОМУ/ЕМУ/СКИ means de cette (comme xxxxx) manière по-королевски = comme un roix по-солдатски = comme un soldat = rapid ou sans raffinements, puritain по-дружески = comme avec un amie по-соседски = de maniere de voisan, comme avec un voisan по-братски = comme avec le frair, en parties égales по-летнему = de manière d'ete (par exemple, quand le soleil brile en iver comme en ete ou quand qqn est abillet trop chaudement). по-французски = comme les francais parlent, i.e. parler francais. по-свойски = comme avec qqn qui est de la maison, à la bonne franquette etc :) And It's not a dative form, it just looks like.

"по-X " is answering on the question "How? How it is?". This is an adverb. Examples: "говорить по-английСКИ" _BUT_ "по английскому языку" "не могу по-другОМУ" _BUT_ "по другому поводу" To sum up, the preposition "по"+ the end of the word "СКИ" or "ОМУ" needs a dash between preposition and adjective. Togetger they works as an adverb. But if you have a word that refers to adjective, it takes away the dash.(по другому поводу, учебник по русскому языку)

Thank you Andy.