With basic terminologies of Bonferroni-type inequalities in the preceding chapter, we can now discuss methods in the construction of Bonferroni-type inequalities, an essential component in probability bounding theory. Chapters 3 and 4 feature two discernible methods in the derivation of Bonferroni-type inequalities. The current chapter focuses on the use of indicator functions and Chapter 4 concentrates on the method of linear programming and optimality.