what is it further classified into?
Observational, radio, Infrared, Optical , Ultraviolet, X-ray and Gamma-ray astronomy.
Astronomy
The main source of information about celestial bodies and other objects is visible light, or more generally electromagnetic radiation. Observational astronomy may be categorized according to the corresponding region of the electromagnetic spectrum on which the observations are made. 
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.
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Astronomy [SEP] Observational astronomy
The main source of information about celestial bodies and other objects is visible light, or more generally electromagnetic radiation. Observational astronomy may be categorized according to the corresponding region of the electromagnetic spectrum on which the observations are made. Some parts of the spectrum can be observed from the Earth's surface, while other parts are only observable from either high altitudes or outside the Earth's atmosphere. Specific information on these subfields is given below.