In the Edo period, local industries arose throughout the country under the encouragement policies of each feudal domain.

Literal

Edo-period [at-に], each-domain [attributive-の] encouragement-policy [by-によって], whole-country-[attributive-の]-various-places [at-に] local-industries [subject-が] arose.

Historical prose. 江戸時代 ('Edo period,' 1603-1868). 藩 ('han, feudal domain') was the territorial administrative unit of Tokugawa Japan. 奨励 ('encouragement, promotion') with 策 ('policy, measure') = 'encouragement policy.' 地場産業 ('local industry, regional industry') refers to crafts and production rooted in a specific locale. 興る ('to arise, to flourish, to rise up') is a literary intransitive verb for the emergence of movements, industries, dynasties.