The institute was established by Karachi University's Department of Mathematics in 1994. It was established as an autonomous research institute with the idea for a space science astrophysics programme and an astronomical observatory was conceived right at the inception of the Karachi University. However, the trace of establishing such institute came in place in 1960, when Professor A.B.A Haleem, Professor of Political Science and Vice-Chancellor of the Karachi University, first obtained and procured the powerful astronomical telescope with relevant equipment from a West-German company. Known as Karachi University Astrophysics Observatory, an astronomical observatory was initiated under the administrative supervision of the Department of Mathematics of the Karachi University. Later in time, the Federal Government of Pakistan built a building to install the observatory which initially belonged to the Department of Mathematics. In 1994, the building and the observatory became a part of the ISPA with Prof. Dr. Jawaid Quamar as its first founding director. Prof. Dr. Jawaid Quamar is credited for leading the institute at an academic and international level as he had attracted many students to do their research under his supervision and he also introduced new programmes in the relevant field in the country. The new metallic dome of the observatory was an evidence of Dr. Quamar's hard work and dedication. Later, after the retirement of Dr. Quamar, Mr. M. Shahid Qureshi took charge of the institute in 2002. He regularized the academic programs at ISPA and lead the institute till 2010. Mr Qureshi earned his PhD from the same institute under the supervision of Prof. Dr. Nasiruddin Khan. In Fact Dr. Qureshi was the third PhD of the institute, first being Prof. Dr. M. Ayub Khan Yousufzai, second Prof. Dr. M. Jawed Iqbal. On June 4, 2015, a brief inaugural session took place at ISPA where, Prof. Dr. Jawaid Quamar inaugurate the ISPA Seminar Library in the memory of "Prof. Dr. Irshad Ahmed Khan Afridi", who was involved in the foundation of ISPA. The new name of ISPA seminar library was approved by the Syndicate of Karachi University.
Undergraduate programme — the institute offers a two years programme. The undergraduate programmes are taught with the advanced courses of engineering. The disciplines are listed below in which the programmes are being offered by the institute:
Post-doctoral research and Doctoral programme — the institute manages the post-doctoral research and doctoral programmes that are expected to be completed in 2–5 years. The degrees are awarded by publishing a thesis supervised by the institute. The doctoral programmes that are offered are listed below.
