DNA is the genetic material of a cell and is copied in the form of pre-mRNA through transcription in eukaryotes. RNA polymerase II is responsible for the transcription of all genes that express proteins. Transcription is a significant source of the stochasticity in gene expression. In this thesis, I discuss the development of a biochemically detailed model of eukaryotic transcription, which includes pre-initiation complex (PIC) assembly, abortive initiation, promoter-proximal pausing and termination as the points that can be slow steps for transcription. The stochastic properties of this model are studied in detail by stochastic simulations with some preliminary mathematical analysis. The results of this model suggest that PIC assembly can play the most significant role in affecting the transcription dynamics. In addition, promoter-proximal pausing has been identified as a potential noise regulatory step in eukaryotic transcription. These results show excellent agreement with many experimental studies. / x, 107 leaves : ill. ; 29 cm