what are it's applications?
It is used for observing the cores of stars.
Neutrino astronomy
Since neutrinos are also created in the cores of stars (as a result of stellar fusion), the core can be observed using neutrino astronomy. 
what area of science did the muslim world excel in Astronomy, mathematics, and medicine. what does the first one refer to? The natural science that studies celestial objects and phenomena. what is it further classified into? Observational, radio, Infrared, Optical , Ultraviolet, X-ray and Gamma-ray astronomy. what are the leading types of the second area? UNANSWERABLE are there any foundations associated with it? Yes, in nutrino astronomy, GALLEX or Gallium Experiment was a radiochemical neutrino detection experiment that ran between 1991 and 1997 at the Laboratori Nazionali del Gran Sasso (LNGS). what does the the kind of astronomy mean? It  is the branch of astronomy that observes astronomical objects with neutrino detectors in special observatories.
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Neutrino astronomy [SEP] Applications
When astronomical bodies, such as the Sun, are studied using light, only the surface of the object can be directly observed. Any light produced in the core of a star will interact with gas particles in the outer layers of the star, taking hundreds of thousands of years to make it to the surface, making it impossible to observe the core directly. Since neutrinos are also created in the cores of stars (as a result of stellar fusion), the core can be observed using neutrino astronomy. Other sources of neutrinos- such as neutrinos released by supernovae- have been detected. There are currently goals to detect neutrinos from other sources, such as active galactic nuclei (AGN), as well as gamma-ray bursts and starburst galaxies.