Zeng's previous theoretical methods for the study of seasonal divisions of atmospheric general circulations and the calculations of monsoons are modified in order to apply to the study of monsoon process more properly and effectively.These modified methods are able to detect the critical of abrupt transition in the atmospheric circulation and the presage day of monsoon by calculating the normalized finite temporal variation.Similarity of two fields etc.from the time series of a functional of the spatial field(the flow in the mathematical terminology).Part I is the application of these methods to the analysis of the climatological mean field,and Part II deals with the analysis of the cases of every individual year and the interannual variations.The major results of Part I are as follows:(1) Our methods can objectively and quantitatively determine the critical of abrupt change of atmospheric general circulation in a region,this can be called as the presage day in the relation with the monsoon and is just 2—4 days earlier than the so-called onset day defined by the conventional meteorological method.(2) In the Northern Hemisphere,in the area of Australia-Asian monsoon system,the of summer monsoon in many key regions is closely related to the abrupt change of atmospheric circulation in that region,the and advance processes are very quick,but in many other regions not related with the abrupt change of circulation and slowly advanced.(3) In the Australia-Asian monsoon area,before the midJune the tropical monsoon branch can be clearly divided into three sub-branches,(a) the region of Warm Pool and its vicinity(onset in the 4th to 5th pentad of April),(b) the region of tropical Indian Ocean(onset first in the late-April to early May),and(c) the region of South China Sea(onset in the second pentad of May in the South and very rapid march to about the Tropic of Cancer in the last pentad of May).The Indian summer monsoon arrives the south-east edge of India in the beginning of June.After mid-July the tropical monsoon branch is unified as a whole subsystem,occupies the whole Indian Peninsula and extends to the South China Sea,30°N of eastern China,and the low latitudes in the vicinity of Warm Pool.The subtropical monsoon branch presents its influence on the eastern Asia and West Pacific in the mid-June,and is prevailing during July and August.Its structure and evolutionary process are relatively complicated,there are three centers in the maps of abrupt change of circulation.One is located north-east to Philippine,the other two in the lower reach of the Yangtze River valley and the Pacific Ocean in the south of Japan.The temperate-frigid monsoon branch is not studied in this paper.(4) The summer monsoon system possesses very pronounced 3-D spatial baroclinic structure.Especially,before the of monsoon in the lower troposphere,there occur already very strong abrupt change of stratosphere general circulation and its seasonal transition from winter to summer,then the abrupt change extends to the whole column of troposphere(although the strength is weakened),and the of monsoon in the low levels of the troposphere takes place.The interactions between stratospheric and the tropospheric circulations and their relation to the of monsoons need further investigation.