강연시간: 13:00-14:00 About two decades ago Connes introduced a pseudodifferential calculus for $C^*$-dynamical systems which provides us with a pseudodifferential calculus on noncommutative tori. This calculus have been widely used in the differential geometry study of noncommutaitve tori initiated by Connes-Tretkoff. Moreover, the notions of pseudodifferential operators with parameters, holomorphic families of pseudodifferential opeartors and complex powers of elliptic pseudodifferential operators on noncommutative tori also play a central role in many of subsequent results of Connes-Tretkoff. Howover, detailed descriptions of these notions have been missing until recently. The aim of this thesis is to give detailed accounts on these notions as an aid in researches initiated by Connes-Tretkoff. We first give a precise explanation of Connes` pseudodifferential calculus on noncommutative tori. To this end we introduce the notion of oscillating integrals for noncommutative tori, which also enables us to deal with the basic properties of Connes` pseudodifferential calculus on noncommtutative tori. Secondly, we define and study the notion of pseudodifferential operators with parameters on noncommutative tori and prove that the resolvent of an elliptic pseudodifferential operator gives rise to a pseudodifferential operator with parameter. The last goal of this thesis is to study holomorphic families of pseudodifferential operators and complex powers of an elliptic pseudodifferential operator on noncommutative tori. In particular, we show that complex powers of an elliptic pseudodifferential operator gives rise to a holomorphic family of pseudodifferential operators.