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A resthouse or a sarai (Hindi for roadside rest-house) that was primarily created for a religious purpose, or as a religious endowment.
A dharmashala (or dharamshala), etymologically, means 'a religious school'. However, the word is generally used in a different context. Most (big) Hindu (and Buddhist) temples in India offer lodging and/or dining facilities for interested individuals or small parties. They are either free (running on donations) or for a very nominal rate. You may donate to the temple to cover your charges if there are any.
Such a facility is called a dharamshala. It is characterized by spartanic (sometimes unclean and pest-ridden) furnishings and quiet and peaceful surroundings. There may be a school under the temple administration in the same locality dispensing Hindu teachings.
'Dharamshala' is essentially a Sanskrit/Hindi word. It is similar to the word 'madarsa' used by Muslims; 'madarsa' however, actually being an Islamic religious school where the holy Koran is taught.
etymology: Dharma = 'religion' + shaalaa = 'school'
However now this is more referred to rest house run by charity society.