The state of astronomical researche in Lviv at the end of the 18th century is elucidated. Some documented facts are given concerning first astronomical observations performed in Lviv. The circumstances of the establishment and construction of the astronomical observatory at the Jesuit collegium (university) are described. The date of the estabtishment of the observatory, 15 May 1771, is found from archival materials. The role of the observatory during the incorporation of Galychyna into Austro-Hungarian empire is investigated. Biographical data are gathered and arranged concerning prominent astronomers and engineers of those times, the lives of which were somehow associated with the Lviv Observatory.