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In this thesis, we study self-similar actions of groupoids on row-finite directed graphs and their associated Cuntz-Krieger algebras. Roughly speaking, if for all scales of parts of the object reiterate the whole, then the object is self-similar. For algebraic objects such as groups or groupoids that have this self-similarity property, we simply call them selfsimilar groups or self-similar groupoids. As an illustration of this self-similarity property, we recall the addition algorithm of integers that we learned from primary school, there is a so-called carrying operation that takes place to deal with addition of larger integers. Analogous to this carrying operation there is so-called a restriction map that encodes self-similarity property.
In the 1980s, Grigorchuk, Gupta, and Sidki were among the pioneers who introduced the concept of self-similar groups to address the question of whether there exist groups with intermediate growth. These groups exhibit self-similarity in their act ....

Row Finite Graphs , Elf Similar Groupoids , Niqueness Theorems , Ideal Structures ,