  We analyze Auslander-Reiten quivers of functorially finite resolving
subcategories.
  Chapter 1 gives a short introduction into the basic definitions and theorems
of Auslander-Reiten theory in A-mod.
  We generalize these definitions and theorems in Chapter 2 and prove
generalizations of the first and one and a half Brauer-Thrall conjecture for
functorially finite resolving subcategories. Moreover, we show that sectional
paths in Auslander-Reiten-quivers are invariants of decompositions of morphisms
into sums of compositions of irreducible morphisms between indecomposable
modules and are strongly connected to irreducible morphisms in subcategories.
  In Chapter 3 we introduce degrees of irreducible morphisms and use this
notion to prove the generalization of the Happel-Preiser-Ringel theorem for
functorially finite resolving subcategories.
  Finally, in Chapter 4, we analyze left stable components of Auslander-Reiten
quivers and find out that their left subgraph types are given by Dynkin
diagrams if and only if the corresponding subcategory is finite. In the
preparation of the proof we discover connected components with certain
properties and name them helical components due to their shape. It turns out
later that these components are the same as coray tubes. In the final section
we discuss under which conditions the length of modules tends to infinity if we
knit to the left in a component and give a complete description of all
connected components in which this is not the case.
