The present invention is a process for producing various types of cannabis extract from harvested cannabis. A quantity of harvested cannabis, which typically includes the inflorescence, floral leaves, and small stems of a flowering cannabis plants, is pre-frozen. The harvested cannabis is first subjected to cryogenic grinding to produce pulverized cannabis. The pulverized cannabis is then subjected to alcohol extraction to produce an initial cannabis extract, which can be subjected to one of several forms of further processing according to the desired chemical profile of the final product. The initial cannabis extract may then be subjected to chemical processing that promote the conversion of THCA to Δ;9 THC; the conversion of THCVA to THCV; the conversion of THCA to cannabinol (“CBN”); or the conversion of THCA to Δ;8-THC.