To my dearest parents and to

This thesis is concerned with higher cluster tilting objects in generalized higher cluster categories and tropical friezes associated with Dynkin diagrams. The generalized cluster category arising from a suitable 3-Calabi-Yau differential graded algebra was introduced by C. Amiot. It is Hom-finite, 2-Calabi-Yau and admits a canonical cluster-tilting object. In this thesis, we extend these results to the case where the initial differential graded algebra is (m + 2)-Calabi-Yau for an arbitrary positive integer m. We show that its associated generalized m-cluster category is Hom-finite, (m + 1)-Calabi-Yau and admits a canonical m-cluster tilting object. In this triangulated category, we obtain a class of m-cluster tilting objects by taking advantage of silting mutation and derived equivalence. For generalized m-cluster categories arising from strongly (m + 2)-Calabi-Yau differential graded algebras, we prove that each almost complete m-cluster tilting P -object admits exactly m + 1 complements with periodicity property. Finally, inspired by Ringel’s work on cluster-additive functions on stable translation quivers, we introduce tropical friezes on 2-Calabi-Yau categories with cluster-tilting object. We show that any tropical frieze on the cluster category of a Dynkin quiver is of a special form and give a proof of a conjecture of Ringel on the form of cluster-additive functions.