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We analyze Auslander-Reiten quivers of functorially finite resolvingsubcategories.  Chapter 1 gives a short introduction into the basic definitions and theoremsof Auslander-Reiten theory in A-mod.  We generalize these definitions and theorems in Chapter 2 and provegeneralizations of the first and one and a half Brauer-Thrall conjecture forfunctorially finite resolving subcategories. Moreover, we show that sectionalpaths in Auslander-Reiten-quivers are invariants of decompositions of morphismsinto sums of compositions of irreducible morphisms between indecomposablemodules and are strongly connected to irreducible morphisms in subcategories.  In Chapter 3 we introduce degrees of irreducible morphisms and use thisnotion to prove the generalization of the Happel-Preiser-Ringel theorem forfunctorially finite resolving subcategories.  Finally, in Chapter 4, we analyze left stable components of Auslander-Reitenquivers and find out that their left subgraph types are given by Dynkindiagrams if and only if the corresponding subcategory is finite. In thepreparation of the proof we discover connected components with certainproperties and name them helical components due to their shape. It turns outlater that these components are the same as coray tubes. In the final sectionwe discuss under which conditions the length of modules tends to infinity if weknit to the left in a component and give a complete description of allconnected components in which this is not the case.

Auslander-Reiten theory in functorially finite resolving subcategories