Coupled cell networks here refer to a group of dynamical systems , called as cells , whose cells are coupled and interact with each other . A directed graph is assigned to each coupled cell network highlighting how cells are influenced by others . An equivalence relation on cells is also shown on the graph . A fundamental question raised in the theory of coupled cell networks refers to interplay between the architecture and the dynamics of these networks and till now , lots of measures have been taken to understand this . Recently , Stewart and Golubitsky et al have presented a well-established framework and many techniques for a systematic dynamics understanding of these kinds of dynamical systems . They introduced a type of 0cm 0cm 0pt" This thesis is split into five chapters as follows. In the first two chapters we introduce basic concepts of the theory of coupled cell networks . In chapter 1 (introduction) we discuss basic preliminaries from equivariant dynamics . Chapter 2 starts with a formal definition of coupled cell networks and its corresponding equivalence relations . In the second section of chapter 2 we define the concept of symmetry groupoid which is a natural extension of group symmetry . Finally , we define coupled cell systems through a family of vector fields , namely admissible vector fields , to a coupled cell network. In chapter 3 , the concept of balanced equivalence relation (or balanced coloring) is introduced . In the first section we show that how these equivalence relations can be used to investigate robust patterns of synchrony . Robustness of patterns here refers to when pattern of synchrony is independent of the specific governed system and thus , it happens for any admissible system . It has been shown that these patterns can be 0cm 0cm 0pt" In chapter 4 we introduce two important families of coupled cell networks; namely quotient networks and homogeneous networks . By having a balanced coloring of a network in hand , we can cluster the cells with the same color and derive a new coupled cell network with less number of cells , namely quotient networks . This network which benefits from its smaller size is able to resemble the dynamics on the original network . In the second section of this chapter homogeneous networks are introduced . This family of networks has an important property , that is , all cells are governed by the same dynamics. Finally , in Chapter 5 (last chapter) we introduce a formalism to compute the normal form of (homogenous) coupled cell systems . Generally , normal form theory employs some near identity changes of coordinates to convert a given dynamical system to a simpler form which has become suitable for local bifurcation analysis . Indeed , normal form theory is a main and efficient tool in analyzing local behavior of dynamical systems . Due to the special forms of coupled cell systems (admissible vector fields) , the methods in