Early astronomical records of comets, supernovae, novae, sunspots and aurorae from Far Eastern dynastic histories together with records from Babylonians cuneiform tablets are compiled and analysed. The present investigation gives new insight into the three following topics in current astronomy and astrophysics.(1) Halley's Comet Past orbits of Halley's Comet since 240 BC are studied in detail using mainly early Chinese observations. The date of perihelion passages are deduced for each return. The only gap in the Chinese records, for the return of 164 BC, is now filled by the discovery of two records on Babylonian tablets. This discovery improves the date of perihelion, which is established as within one week of Nov 16 in 164 BC. We are now confident that every return of Halley's Comet from 240 BC onwards has been recorded.(2) Supernovae and Novae A catalogue of historical supernovae and novae is compiled. Descriptions regarding the position of the eight well known supemovae SN 185, 386, 393, 1006, 1054, 1181, 1572 and 1604 are re-evaluated in term of recent studies. The spurious supernova SN 1408 is discussed in detail and found that there is insufficient evidence supporting a supernova interpretation. The positions of 26 well recorded historical novae are discussed in depth and their coordinates are deduced. (3) Solar Variability Catalogues of naked-eye sunspots and aurorae are compiled from Far Eastern sources. Analysis of these records suggests an average period of about 10 years for the basic solar cycle. Observational factors such as variation with the phases of the Moon are also discussed. A comparison of these data with other proxy indicators like (^14)C and (^10)Beshows a similar trend in the behaviour of the Sun over the last two thousand years.