In this thesis, on the basis of the asymmetrical charge distribution of E. coli topoisomerase I, I developed a new rapid procedure to purify E. coli DNA topoismoerase I in the milligram range. The new procedure includes using both cation- and anion-exchange columns, i.e., SP-sepharose FF and Q-sepharose FF columns. E. coli topoisomerase I purified here is free of nuclease contamination. The kinetic constants of the DNA relaxation reaction of E. coli DNA topoisomerase I were determined as well. I also used isothermal titration calorimetry to investigate the energetics of DNA supercoiling by using the unwinding properties of DNA intercalators, ethidium and daunomycin. After comparing the enthalpy changes of these DNA intercalators binding to supercoiled and nicked or relaxed plasmid DNA pXXZ06, I determined the DNA supercoiling enthalpy is about 12 kcal/mol per turn of DNA supercoil, which is in good agreement with the previously published results.